1
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Wang Z, Ren J. Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport. PHYSICAL REVIEW LETTERS 2024; 132:207101. [PMID: 38829089 DOI: 10.1103/physrevlett.132.207101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Revised: 09/06/2023] [Accepted: 04/11/2024] [Indexed: 06/05/2024]
Abstract
Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.
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Affiliation(s)
- Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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2
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Sangchai T, Al Shehimy S, Penocchio E, Ragazzon G. Artificial Molecular Ratchets: Tools Enabling Endergonic Processes. Angew Chem Int Ed Engl 2023; 62:e202309501. [PMID: 37545196 DOI: 10.1002/anie.202309501] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 08/03/2023] [Accepted: 08/04/2023] [Indexed: 08/08/2023]
Abstract
Non-equilibrium chemical systems underpin multiple domains of contemporary interest, including supramolecular chemistry, molecular machines, systems chemistry, prebiotic chemistry, and energy transduction. Experimental chemists are now pioneering the realization of artificial systems that can harvest energy away from equilibrium. In this tutorial Review, we provide an overview of artificial molecular ratchets: the chemical mechanisms enabling energy absorption from the environment. By focusing on the mechanism type-rather than the application domain or energy source-we offer a unifying picture of seemingly disparate phenomena, which we hope will foster progress in this fascinating domain of science.
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Affiliation(s)
- Thitiporn Sangchai
- University of Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - Shaymaa Al Shehimy
- University of Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - Emanuele Penocchio
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA
| | - Giulio Ragazzon
- University of Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, 67000, Strasbourg, France
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3
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Gupt N, Ghosh S, Ghosh A. Top-ranked cycle flux network analysis of molecular photocells. Phys Rev E 2023; 108:034305. [PMID: 37849165 DOI: 10.1103/physreve.108.034305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 08/22/2023] [Indexed: 10/19/2023]
Abstract
We introduce a top-ranked cycle flux ranking scheme of network analysis to assess the performance of molecular junction solar cells. By mapping the Lindblad master equation to the quantum-transition network, we propose a microscopic Hamiltonian description underpinning the rate equations commonly used to characterize molecular photocells. Our approach elucidates the paramount significance of edge flux and unveils two pertinent electron transfer pathways that play equally important roles in robust photocurrent generation. Furthermore, we demonstrate that nonradiative loss processes impede the maximum power efficiency of photocells, which may otherwise be above the Curzon-Ahlborn limit. These findings shed light on the intricate functionalities that govern molecular photovoltaics and offer a comprehensive approach to address them in a systematic way.
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Affiliation(s)
- Nikhil Gupt
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
| | - Shuvadip Ghosh
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
| | - Arnab Ghosh
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
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4
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Das D, Pradhan P, Chatterjee S. Optimum transport in systems with time-dependent drive and short-ranged interactions. Phys Rev E 2023; 108:034107. [PMID: 37849159 DOI: 10.1103/physreve.108.034107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 08/14/2023] [Indexed: 10/19/2023]
Abstract
We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.
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Affiliation(s)
- Deepsikha Das
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Sakuntala Chatterjee
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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5
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Zhang Z, Lu Z. Nonequilibrium Theoretical Framework and Universal Design Principles of Oscillation-Driven Catalysis. J Phys Chem Lett 2023; 14:7541-7548. [PMID: 37586077 DOI: 10.1021/acs.jpclett.3c01677] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
At stationary environmental conditions, a catalyst's reaction kinetics may be restricted by its available designs and thermodynamic laws. Thus, its stationary performances may experience practical or theoretical restraints (e.g., catalysts cannot invert the spontaneous direction of a chemical reaction). However, many works have reported that if environments change rapidly, catalysts can be driven away from stationary states and exhibit anomalous performance. We present a general geometric nonequilibrium theory to explain anomalous catalytic behaviors driven by rapidly oscillating environments where stationary-environment restraints are broken. It leads to a universal design principle of novel catalysts with oscillation-pumped performances. Even though a single free energy landscape cannot describe catalytic kinetics at various environmental conditions, we propose a novel control-conjugate landscape to encode the reaction kinetics over a range of control parameters λ, inspired by the Arrhenius form. The control-conjugate landscape significantly simplifies the design principle applicable to large-amplitude environmental oscillations.
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Affiliation(s)
- Zhongmin Zhang
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
| | - Zhiyue Lu
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
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6
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Bilancioni M, Esposito M, Penocchio E. A [3]-catenane non-autonomous molecular motor model: Geometric phase, no-pumping theorem, and energy transduction. J Chem Phys 2023; 158:224104. [PMID: 37310874 DOI: 10.1063/5.0151625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 05/17/2023] [Indexed: 06/15/2023] Open
Abstract
We study a model of a synthetic molecular motor-a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one-subjected to time-dependent driving using stochastic thermodynamics. The model presents nontrivial features due to the two interacting small macrocycles but is simple enough to be treated analytically in limiting regimes. Among the results obtained, we find a mapping into an equivalent [2]-catenane that reveals the implications of the no-pumping theorem stating that to generate net motion of the small macrocycles, both energies and barriers need to change. In the adiabatic limit (slow driving), we fully characterize the motor's dynamics and show that the net motion of the small macrocycles is expressed as a surface integral in parameter space, which corrects previous erroneous results. We also analyze the performance of the motor subjected to step-wise driving protocols in the absence and presence of an applied load. Optimization strategies for generating large currents and maximizing free energy transduction are proposed. This simple model provides interesting clues into the working principles of non-autonomous molecular motors and their optimization.
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Affiliation(s)
- Massimo Bilancioni
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City 1511, Luxembourg
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City 1511, Luxembourg
| | - Emanuele Penocchio
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City 1511, Luxembourg
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
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7
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Zhang Z, Du V, Lu Z. Energy landscape design principle for optimal energy harnessing by catalytic molecular machines. Phys Rev E 2023; 107:L012102. [PMID: 36797891 DOI: 10.1103/physreve.107.l012102] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 12/27/2022] [Indexed: 06/18/2023]
Abstract
Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harness energy from the oscillatory bath and use it to drive other processes. Using an alternative geometrical approach, under fast temperature oscillation, we derive a general design principle for obtaining the optimal catalytic energy landscape that can harness energy from a temperature-oscillatory bath and use it to invert a spontaneous reaction. By driving the reaction against the spontaneous direction, the catalysts convert low free-energy product molecules to high free-energy reactant molecules. The design principle, derived for arbitrary cyclic catalysts, is expressed as a simple quadratic objective function that only depends on the reaction activation energies, and is independent of the temperature protocol. Since the reaction activation energies are directly accessible by experimental measurements, the objective function can be directly used to guide the search for optimal energy-harvesting catalysts.
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Affiliation(s)
- Zhongmin Zhang
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
| | - Vincent Du
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
| | - Zhiyue Lu
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
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8
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Wang Z, Chen J, Ren J. Geometric heat pump and no-go restrictions of nonreciprocity in modulated thermal diffusion. Phys Rev E 2022; 106:L032102. [PMID: 36266907 DOI: 10.1103/physreve.106.l032102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
Thermodynamics strongly restricts the direction of heat flow in static macroscopic thermal diffusive systems. To overcome this constraint, spatiotemporal modulated systems are used instead. Here, we unveil the underlying geometric heat pump effect in macroscopic driven thermal diffusion, which is crucial for achieving thermal nonreciprocity. We obtain a geometric expression to formulate the nontrivial current in a driven system, manifesting as an extra pumped heat ably diffusing from cold to hot that has no analogy in static setups. Moreover, we analyze the underlying geometric curvature of driven diffusive systems and derive no-pumping restriction theorems that constrain the thermal action under modulations and guide the optimization of driving protocols. Following the restrictions from geometry, we finally implement a minimum experiment and observe the predicted pumped heat in the absence of thermal bias at every instant, which is independent of the driving speed in the adiabatic limit, clearly validating the geometric theory. An extension of the geometric pump effect and no-pumping restrictions to macroscopic mass diffusion governed by Fick's law is also discussed. These results pave the way for designing and implementing nonreciprocal and topological diffusive systems under spatiotemporal modulations.
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Affiliation(s)
- Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jiangzhi Chen
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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9
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Dechant A, Sasa SI, Ito S. Geometric decomposition of entropy production into excess, housekeeping, and coupling parts. Phys Rev E 2022; 106:024125. [PMID: 36109899 DOI: 10.1103/physreve.106.024125] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
For a generic overdamped Langevin dynamics driven out of equilibrium by both time-dependent and nonconservative forces, the entropy production rate can be decomposed into two positive terms, termed excess and housekeeping entropy. However, this decomposition is not unique: There are two distinct decompositions, one due to Hatano and Sasa, the other one due to Maes and Netočný. Here we establish the connection between these two decompositions and provide a simple, geometric interpretation. We show that this leads to a decomposition of the entropy production rate into three positive terms, which we call the excess, housekeeping, and coupling part, respectively. The coupling part characterizes the interplay between the time-dependent and nonconservative forces. We also derive thermodynamic uncertainty relations for the excess and housekeeping entropy in both the Hatano-Sasa and Maes-Netočný decomposition and show that all quantities obey integral fluctuation theorems. We illustrate the decomposition into three terms using a solvable example of a dragged particle in a nonconservative force field.
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Affiliation(s)
- Andreas Dechant
- Department of Physics no. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Shin-Ichi Sasa
- Department of Physics no. 1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Sosuke Ito
- Universal Biology Institute, The University of Tokyo, Tokyo 113-0033, Japan
- JST, PRESTO, Saitama 332-0012, Japan
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10
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Strand NE, Vroylandt H, Gingrich T. Computing time-periodic steady-state currents via the time evolution of tensor network states. J Chem Phys 2022; 157:054104. [DOI: 10.1063/5.0099741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group (DMRG) algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Though trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial.
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Affiliation(s)
- Nils E Strand
- Chemistry, Northwestern University, United States of America
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11
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Wang L, Wang Z, Wang C, Ren J. Cycle Flux Ranking of Network Analysis in Quantum Thermal Devices. PHYSICAL REVIEW LETTERS 2022; 128:067701. [PMID: 35213197 DOI: 10.1103/physrevlett.128.067701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Revised: 12/08/2021] [Accepted: 01/19/2022] [Indexed: 06/14/2023]
Abstract
Manipulating quantum thermal transport relies on uncovering the principle working cycles of quantum devices. Here we introduce the cycle flux ranking of network analysis to nonequilibrium thermal devices characterized as a quantum-transition network. To excavate the principal mechanism out of complex transport behaviors, we decompose the network into cycle trajectories, collect the cycle fluxes by algebraic graph theory, and select top-ranked cycle fluxes, i.e., the cycle trajectories with highest probabilities. We exemplify the cycle flux ranking in typical quantum device models, e.g., a thermal-drag spin-Seebeck pump and a quantum thermal transistor. Top-ranked cycle trajectories indeed elucidate the principal working mechanisms. Therefore, cycle flux ranking provides an alternative perspective that naturally describes the working cycle corresponding to the main functionality of quantum thermal devices, which would further guide the device optimization with desired performance.
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Affiliation(s)
- Luqin Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Zi Wang
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Chen Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, Zhejiang, People's Republic of China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Lab on Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
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12
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Kolchinsky A, Wolpert DH. Entropy production given constraints on the energy functions. Phys Rev E 2021; 104:034129. [PMID: 34654169 DOI: 10.1103/physreve.104.034129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 08/25/2021] [Indexed: 11/07/2022]
Abstract
We consider the problem of driving a finite-state classical system from some initial distribution p to some final distribution p^{'} with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions E. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in {p,p^{'}} and a graph-theoretic property defined in terms of E. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation p→p^{'} can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.
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13
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Remlein B, Seifert U. Optimality of nonconservative driving for finite-time processes with discrete states. Phys Rev E 2021; 103:L050105. [PMID: 34134247 DOI: 10.1103/physreve.103.l050105] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Accepted: 05/11/2021] [Indexed: 11/07/2022]
Abstract
An optimal finite-time process drives a given initial distribution to a given final one in a given time at the lowest cost as quantified by total entropy production. We prove that for a system with discrete states this optimal process involves nonconservative driving, i.e., a genuine driving affinity, in contrast to the case of a system with continuous states. In a multicyclic network, the optimal driving affinity is bounded by the number of states within each cycle. If the driving affects forward and backwards rates nonsymmetrically, the bound additionally depends on a structural parameter characterizing this asymmetry.
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Affiliation(s)
- Benedikt Remlein
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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14
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Hino Y, Hayakawa H. Fluctuation relations for adiabatic pumping. Phys Rev E 2020; 102:012115. [PMID: 32795070 DOI: 10.1103/physreve.102.012115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Accepted: 05/28/2020] [Indexed: 06/11/2023]
Abstract
We derive an extended fluctuation relation for an open system coupled with two reservoirs under adiabatic one-cycle modulation. We confirm that the geometrical phase caused by the Berry-Sinitsyn-Nemenman curvature in the parameter space generates non-Gaussian fluctuations. This non-Gaussianity is enhanced for the instantaneous fluctuation relation when the bias between the two reservoirs disappears.
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Affiliation(s)
- Yuki Hino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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15
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Funo K, Lambert N, Nori F, Flindt C. Shortcuts to Adiabatic Pumping in Classical Stochastic Systems. PHYSICAL REVIEW LETTERS 2020; 124:150603. [PMID: 32357046 DOI: 10.1103/physrevlett.124.150603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be nonzero even in the absence of a bias. However, as the driving speed is increased, nonadiabatic excitations gradually reduce the pumped charge, thereby limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the method is also robust against moderate fluctuations of the control field. We provide a geometric interpretation of the control protocol and analyze the thermodynamic cost of implementing it. Our findings can be realized using current technology and potentially enable fast pumping of charge or heat in quantum dots, as well as in other stochastic systems from physics, chemistry, and biology.
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Affiliation(s)
- Ken Funo
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Neill Lambert
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Franco Nori
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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16
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Takahashi K, Fujii K, Hino Y, Hayakawa H. Nonadiabatic Control of Geometric Pumping. PHYSICAL REVIEW LETTERS 2020; 124:150602. [PMID: 32357045 DOI: 10.1103/physrevlett.124.150602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the nontrivial part of the current is possible even in the nonadiabatic regime. The exact result allows us to find a smooth connection between the adiabatic Berry phase theory at low frequencies and the Floquet theory at high frequencies. We also study how to control the geometric current. Using the method of shortcuts to adiabaticity with the aid of an assisting field, we illustrate that it enhances the current.
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Affiliation(s)
- Kazutaka Takahashi
- Institute of Innovative Research, Tokyo Institute of Technology, Kanagawa 226-8503, Japan
| | - Keisuke Fujii
- Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan and iTHEMS Program, RIKEN, Saitama 351-0198, Japan
| | - Yuki Hino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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17
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Shpielberg O, Nemoto T. Imitating nonequilibrium steady states using time-varying equilibrium force in many-body diffusive systems. Phys Rev E 2019; 100:032104. [PMID: 31640012 DOI: 10.1103/physreve.100.032104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2019] [Indexed: 11/07/2022]
Abstract
An equivalence between nonequilibrium steady states (NESS) driven by a time-independent force and stochastic pumps (SP) stirred by a time-varying conservative force is studied for general many-body diffusive systems. When the particle density and current of NESS are imitated by SP time-averaged counterparts, we prove that the entropy production rate in the SP is always greater than that of the NESS, provided that the conductivity of the particle current is concave as a function of the particle density. Searching for a SP protocol that saturates the entropy production bound reveals an unexpected connection with traffic waves, where a high density region propagates against the direction of the particle current.
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Affiliation(s)
- Ohad Shpielberg
- Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
| | - Takahiro Nemoto
- Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France
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18
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Palese LL. Cytochrome c oxidase structures suggest a four-state stochastic pump mechanism. Phys Chem Chem Phys 2019; 21:4822-4830. [DOI: 10.1039/c8cp07365a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
A simple stochastic model for a cytochrome c oxidase proton pump.
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Affiliation(s)
- Luigi Leonardo Palese
- University of Bari “Aldo Moro”
- Department of Basic Medical Sciences
- Neurosciences and Sense Organs (SMBNOS)
- Bari
- Italy
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19
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Solon AP, Horowitz JM. Phase Transition in Protocols Minimizing Work Fluctuations. PHYSICAL REVIEW LETTERS 2018; 120:180605. [PMID: 29775356 DOI: 10.1103/physrevlett.120.180605] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 06/08/2023]
Abstract
For two canonical examples of driven mesoscopic systems-a harmonically trapped Brownian particle and a quantum dot-we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal-work protocols, which therefore never become quasistatic.
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Affiliation(s)
- Alexandre P Solon
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
| | - Jordan M Horowitz
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
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20
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Pezzato C, Cheng C, Stoddart JF, Astumian RD. Mastering the non-equilibrium assembly and operation of molecular machines. Chem Soc Rev 2018; 46:5491-5507. [PMID: 28338143 DOI: 10.1039/c7cs00068e] [Citation(s) in RCA: 203] [Impact Index Per Article: 33.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
In mechanically interlocked compounds, such as rotaxanes and catenanes, the molecules are held together by mechanical rather than chemical bonds. These compounds can be engineered to have several well-defined mechanical states by incorporating recognition sites between the different components. The rates of the transitions between the recognition sites can be controlled by introducing steric "speed bumps" or electrostatically switchable gates. A mechanism for the absorption of energy can also be included by adding photoactive, catalytically active, or redox-active recognition sites, or even charges and dipoles. At equilibrium, these Mechanically Interlocked Molecules (MIMs) undergo thermally activated transitions continuously between their different mechanical states where every transition is as likely as its microscopic reverse. External energy, for example, light, external modulation of the chemical and/or physical environment or catalysis of an exergonic reaction, drives the system away from equilibrium. The absorption of energy from these processes can be used to favour some, and suppress other, transitions so that completion of a mechanical cycle in a direction in which work is done on the environment - the requisite of a molecular machine - is more likely than completion in a direction in which work is absorbed from the environment. In this Tutorial Review, we discuss the different design principles by which molecular machines can be engineered to use different sources of energy to carry out self-organization and the performance of work in their environments.
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Affiliation(s)
- Cristian Pezzato
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA.
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21
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Astumian RD. Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment. Chem Commun (Camb) 2018; 54:427-444. [PMID: 29242862 DOI: 10.1039/c7cc06683j] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
In the absence of input energy, a chemical reaction in a closed system ineluctably relaxes toward an equilibrium state governed by a Boltzmann distribution. The addition of a catalyst to the system provides a way for more rapid equilibration toward this distribution, but the catalyst can never, in and of itself, drive the system away from equilibrium. In the presence of external fluctuations, however, a macromolecular catalyst (e.g., an enzyme) can absorb energy and drive the formation of a steady state between reactant and product that is not determined solely by their relative energies. Due to the ubiquity of non-equilibrium steady states in living systems, the development of a theory for the effects of external fluctuations on chemical systems has been a longstanding focus of non-equilibrium thermodynamics. The theory of stochastic pumping has provided insight into how a non-equilibrium steady-state can be formed and maintained in the presence of dissipation and kinetic asymmetry. This effort has been greatly enhanced by a confluence of experimental and theoretical work on synthetic molecular machines designed explicitly to harness external energy to drive non-equilibrium transport and self-assembly.
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Affiliation(s)
- R D Astumian
- Department of Physics, University of Maine, Orono, ME 04469, USA.
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22
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Frezzato D. Dissipation, lag, and drift in driven fluctuating systems. Phys Rev E 2018; 96:062113. [PMID: 29347343 DOI: 10.1103/physreve.96.062113] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Indexed: 11/07/2022]
Abstract
This work deals with thermostated fluctuating systems subjected to driven transformations of the internal energetics. The main focus is on generally multidimensional systems with continuous configurational degrees of freedom over which overdamped Markovian fluctuations take place (diffusive regime of the motion). Mutual bounds are established between the average energy dissipation, the deviation between nonequilibrium probability density and underlying equilibrium distribution due to the system's lag, and the statistical properties of the components of the directed flow induced by the transformation itself. The directed flow is here expressed in terms of time-dependent "drift velocity" associated with the probability current in a advection-like formulation of the nonstationary Fokker-Planck equation. Consideration of the drift makes that the bounds achieved here extend the inequality derived by Vaikuntanathan and Jarzynski [Europhys. Lett. 87, 60005 (2009)EULEEJ0295-507510.1209/0295-5075/87/60005] involving only dissipation and lag. The key relations are then specified for the so-called stochastic pumps, i.e., systems that reach a periodic steady state in response of cyclic transformations and that are prototypes of nonautonomous dissipative converters of input energy into directed motion; a one-dimensional case model is adopted to illustrate the main features. Complementary results concerning bounds between the evolution rates of dissipation and lag, valid for both overdamped and underdamped dynamics, are also presented.
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Affiliation(s)
- Diego Frezzato
- Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131, Padova, Italy
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23
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Rosas A, Van den Broeck C, Lindenberg K. Stochastic thermodynamics for a periodically driven single-particle pump. Phys Rev E 2017; 96:052135. [PMID: 29347780 DOI: 10.1103/physreve.96.052135] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Indexed: 06/07/2023]
Abstract
We present the stochastic thermodynamic analysis of a time-periodic single-particle pump, including explicit results for flux, thermodynamic force, entropy production, work, heat, and efficiency. These results are valid far from equilibrium. The deviations from the linear (Onsager) regime are discussed.
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Affiliation(s)
- Alexandre Rosas
- Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900, João Pessoa, Brazil
| | | | - Katja Lindenberg
- Department of Chemistry and Biochemistry, and BioCircuits Institute, University of California San Diego, La Jolla, California 92093-0340, USA
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24
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Ray S, Barato AC. Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes. Phys Rev E 2017; 96:052120. [PMID: 29347722 DOI: 10.1103/physreve.96.052120] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Indexed: 06/07/2023]
Abstract
Periodic driving is used to operate machines that go from standard macroscopic engines to small nonequilibrium microsized systems. Two classes of such systems are small heat engines driven by periodic temperature variations, and molecular pumps driven by external stimuli. Well-known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affinities, and symmetry relations for the Onsager coefficients from linear-response theory. For nonequilibrium steady states, the Onsager reciprocity relations can be obtained from the more general fluctuation theorem for the currents. We prove a fluctuation theorem for the currents for periodically driven systems. We show that this fluctuation theorem implies a fluctuation dissipation relation, symmetry relations for Onsager coefficients, and further relations for nonlinear response coefficients. The setup in this paper is more general than previous studies, i.e., our results are valid for both heat engines and molecular pumps. The external protocol is assumed to be stochastic in our framework, which leads to a particularly convenient way to treat periodically driven systems.
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Affiliation(s)
- Somrita Ray
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Strasse 38, 01187 Dresden, Germany
| | - Andre C Barato
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Strasse 38, 01187 Dresden, Germany
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25
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Stochastic resonance in a proton pumping Complex I of mitochondria membranes. Sci Rep 2017; 7:12405. [PMID: 28963519 PMCID: PMC5622088 DOI: 10.1038/s41598-017-12746-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Accepted: 09/15/2017] [Indexed: 11/24/2022] Open
Abstract
We make use of the physical mechanism of proton pumping in the so-called Complex I within mitochondria membranes. Our model is based on sequential charge transfer assisted by conformational changes which facilitate the indirect electron-proton coupling. The equations of motion for the proton operators are derived and solved numerically in combination with the phenomenological Langevin equation describing the periodic conformational changes. We show that with an appropriate set of parameters, protons can be transferred against an applied voltage. In addition, we demonstrate that only the joint action of the periodic energy modulation and thermal noise leads to efficient uphill proton transfer, being a manifestation of stochastic resonance.
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26
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Watanabe KL, Hayakawa H. Geometric fluctuation theorem for a spin-boson system. Phys Rev E 2017; 96:022118. [PMID: 28950528 DOI: 10.1103/physreve.96.022118] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.
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Affiliation(s)
- Kota L Watanabe
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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27
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Rotskoff GM. Mapping current fluctuations of stochastic pumps to nonequilibrium steady states. Phys Rev E 2017; 95:030101. [PMID: 28415360 DOI: 10.1103/physreve.95.030101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Indexed: 06/07/2023]
Abstract
We show that current fluctuations in a stochastic pump can be robustly mapped to fluctuations in a corresponding time-independent nonequilibrium steady state. We thus refine a recently proposed mapping so that it ensures equivalence of not only the averages, but also optimal representation of fluctuations in currents and density. Our mapping leads to a natural decomposition of the entropy production in stochastic pumps similar to the "housekeeping" heat. As a consequence of the decomposition of entropy production, the current fluctuations in weakly perturbed stochastic pumps are shown to satisfy a universal bound determined by the steady state entropy production.
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Affiliation(s)
- Grant M Rotskoff
- Biophysics Graduate Group, University of California, Berkeley, California 94720, USA
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28
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Rahav S. Validity of the no-pumping theorem in systems with finite-range interactions between particles. Phys Rev E 2017; 95:012159. [PMID: 28208507 DOI: 10.1103/physreve.95.012159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Indexed: 06/06/2023]
Abstract
The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle systems with zero-range interactions. Interestingly, it is known that the theorem is violated by systems with exclusion interactions. These two paradigmatic interactions differ by two qualitative aspects: the range of interactions and the dependence of branching fractions on the state of the system. In this work two different models are studied in order to identify the qualitative property of the interaction that leads to breakdown of no pumping. A model with finite-range interaction is shown analytically to satisfy no pumping. In contrast, a model in which the interaction affects the probabilities of reaching different sites, given that a particle is making a transition, is shown numerically to violate the no-pumping theorem. The results suggest that systems with interactions that lead to state-dependent branching fractions do not satisfy the no-pumping theorem.
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Affiliation(s)
- Saar Rahav
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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29
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Catanzaro MJ, Chernyak VY, Klein JR. Stochastic dynamics of extended objects in driven systems: I. Higher-dimensional currents in the continuous setting. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.08.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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30
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Stochastic dynamics of extended objects in driven systems II: Current quantization in the low-temperature limit. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.08.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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31
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Sinitsyn NA, Pershin YV. The theory of spin noise spectroscopy: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:106501. [PMID: 27615689 DOI: 10.1088/0034-4885/79/10/106501] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical spin noise spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside examples of their applications.
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Affiliation(s)
- Nikolai A Sinitsyn
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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32
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Allahverdyan AE, Babajanyan SG, Martirosyan NH, Melkikh AV. Adaptive Heat Engine. PHYSICAL REVIEW LETTERS 2016; 117:030601. [PMID: 27472104 DOI: 10.1103/physrevlett.117.030601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 06/06/2023]
Abstract
A major limitation of many heat engines is that their functioning demands on-line control and/or an external fitting between the environmental parameters (e.g., temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence, no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that make the bath temperatures closer. We determine resources of adaptation and relate them to the prior information available about the environment.
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Affiliation(s)
- A E Allahverdyan
- Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia
| | - S G Babajanyan
- Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia
| | - N H Martirosyan
- Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia
| | - A V Melkikh
- Ural Federal University, Mira Street 19, Yekaterinburg 620002, Russia
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33
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Chatterjee R, Chatterjee S, Pradhan P. Symmetric exclusion processes on a ring with moving defects. Phys Rev E 2016; 93:062124. [PMID: 27415225 DOI: 10.1103/physreve.93.062124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Indexed: 11/07/2022]
Abstract
We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders-a generalization of the model we proposed earlier [Phys. Rev. E 89, 022138 (2014)PLEEE81539-375510.1103/PhysRevE.89.022138]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.
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Affiliation(s)
- Rakesh Chatterjee
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Sakuntala Chatterjee
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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34
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Einax M, Nitzan A. Maximum efficiency of state-space models of nanoscale energy conversion devices. J Chem Phys 2016; 145:014108. [DOI: 10.1063/1.4955160] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Chaudhuri D, Raju A, Dhar A. Pumping single-file colloids: Absence of current reversal. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:050103. [PMID: 26066100 DOI: 10.1103/physreve.91.050103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Indexed: 06/04/2023]
Abstract
We consider the single-file motion of colloidal particles interacting via short-range repulsion and placed in a traveling wave potential that varies periodically in time and space. Under suitable driving conditions, a directed time-averaged flow of colloids is generated. We obtain analytic results for the model using a perturbative approach to solve the Fokker-Planck equations. The predictions show good agreement with numerical simulations. We find peaks in the time-averaged directed current as a function of driving frequency, wavelength, and particle density and discuss possible experimental realizations. Surprisingly, unlike a closely related exclusion dynamics on a lattice, the directed current in the present model does not show current reversal with density. A linear response formula relating current response to equilibrium correlations is also proposed.
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Affiliation(s)
- Debasish Chaudhuri
- Indian Institute of Technology, Hyderabad, Yeddumailaram 502205, Andhra Pradesh, India
| | - Archishman Raju
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - Abhishek Dhar
- International Centre for Theoretical Sciences, TIFR, IISc Campus, Bangalore 560012, India
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36
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Esposito M, Parrondo JMR. Stochastic thermodynamics of hidden pumps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052114. [PMID: 26066126 DOI: 10.1103/physreve.91.052114] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/04/2023]
Abstract
We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping mechanism is not accessible, will observe a Markov chain satisfying local detailed balance with an emerging effective force induced by the hidden pump. Due to the reversibility of the pump, the actual entropy production turns out to be lower than the coarse-grained entropy production estimated from the flows and affinities of the resulting Markov chain. Moreover, in presence of a large time scale separation between the fast-pumping dynamics and the slow-network dynamics, a finite current with zero dissipation may be produced. We make use of these general results to build a synthetase-like kinetic scheme able to reversibly produce high free-energy molecules at a finite rate and a rotatory motor achieving 100% efficiency at finite speed.
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Affiliation(s)
- Massimiliano Esposito
- Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Juan M R Parrondo
- Departamento de Fisica Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
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37
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Asban S, Rahav S. No-pumping theorem for many particle stochastic pumps. PHYSICAL REVIEW LETTERS 2014; 112:050601. [PMID: 24580580 DOI: 10.1103/physrevlett.112.050601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2013] [Indexed: 06/03/2023]
Abstract
Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett. 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional no-pumping theorem.
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Affiliation(s)
- Shahaf Asban
- Faculty of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Saar Rahav
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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38
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Chatterjee R, Chatterjee S, Pradhan P, Manna SS. Interacting particles in a periodically moving potential: traveling wave and transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022138. [PMID: 25353453 DOI: 10.1103/physreve.89.022138] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2013] [Indexed: 06/04/2023]
Abstract
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles where the diffusion dynamics is locally modified at a uniformly moving defect site, mimicking the effect of the periodically moving external potential. The model, though simple, exhibits remarkably rich features in particle transport, such as polarity reversal and double peaks in particle current upon variation of defect velocity and particle density. By tuning these variables, the most efficient transport can be achieved in either direction along the ring. These features can be understood in terms of a traveling density wave propagating in the system. Our results could be experimentally tested, e.g., in a system of colloidal particles driven by a moving optical tweezer.
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Affiliation(s)
- Rakesh Chatterjee
- CMP Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India
| | - Sakuntala Chatterjee
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
| | - S S Manna
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
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39
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Krivov SV. Method to describe stochastic dynamics using an optimal coordinate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062131. [PMID: 24483410 DOI: 10.1103/physreve.88.062131] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2013] [Indexed: 06/03/2023]
Abstract
A general method to describe the stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems: the determination of an optimal coordinate for the description of stochastic dynamics; the reconstruction of time from an ensemble of stochastic trajectories; and the decomposition of stationary stochastic dynamics into eigenmodes which do not decay exponentially with time. The problems are solved by introducing additive eigenvectors which are transformed by a stochastic matrix in a simple way - every component is translated by a constant distance. Such solutions have peculiar properties. For example, an optimal coordinate for stochastic dynamics with detailed balance is a multivalued function. An optimal coordinate for a random walk on a line corresponds to the conventional eigenvector of the one-dimensional Dirac equation. The equation for the optimal coordinate in a slowly varying potential reduces to the Hamilton-Jacobi equation for the action function.
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Affiliation(s)
- Sergei V Krivov
- Astbury Center for Structural Molecular Biology, University of Leeds, Leeds, LS2 9JT, United Kingdom
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40
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Perez-Carrasco R, Sancho JM. Theoretical study of a molecular turbine. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042705. [PMID: 24229211 DOI: 10.1103/physreve.88.042705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2013] [Revised: 08/20/2013] [Indexed: 06/02/2023]
Abstract
We present an analytic and stochastic simulation study of a molecular engine working with a flux of particles as a turbine. We focus on the physical observables of velocity, flux, power, and efficiency. The control parameters are the external conservative force and the particle densities. We revise a simpler previous study by using a more realistic model containing multiple equidistant vanes complemented by stochastic simulations of the particles and the turbine. Here we show that the effect of the thermal fluctuations into the flux and the efficiency of these nanometric devices are relevant to the working scale of the system. The stochastic simulations of the Brownian motion of the particles and turbine support the simplified analytical calculations performed.
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Affiliation(s)
- R Perez-Carrasco
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom and Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Carrer Martí Franqués, 1, 08028 Barcelona, Spain
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41
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Wang Z, Hou R, Efremov A. Directional fidelity of nanoscale motors and particles is limited by the 2nd law of thermodynamics—Via a universal equality. J Chem Phys 2013; 139:035105. [DOI: 10.1063/1.4813626] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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42
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Horowitz JM, Sagawa T, Parrondo JMR. Imitating chemical motors with optimal information motors. PHYSICAL REVIEW LETTERS 2013; 111:010602. [PMID: 23862988 DOI: 10.1103/physrevlett.111.010602] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2012] [Indexed: 06/02/2023]
Abstract
To induce transport, detailed balance must be broken. A common mechanism is to bias the dynamics with a thermodynamic fuel, such as chemical energy. An intriguing, alternative strategy is for a Maxwell demon to effect the bias using feedback. We demonstrate that these two different mechanisms lead to distinct thermodynamics by contrasting a chemical motor and information motor with identical dynamics. To clarify this difference, we study both models within one unified framework, highlighting the role of the interaction between the demon and the motor. This analysis elucidates the manner in which information is incorporated into a physical system.
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Affiliation(s)
- Jordan M Horowitz
- Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, 28040 Madrid, Spain
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Akimov AV, Mandal D, Chernyak VY, Sinitsyn NA. Directed motion of periodically driven molecular motors: A graph-theoretical approach. J Chem Phys 2013; 138:024109. [DOI: 10.1063/1.4774270] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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Mandal D, Jarzynski C. Hybrid models of molecular machines and the no-pumping theorem. J Chem Phys 2012; 137:234104. [PMID: 23267468 DOI: 10.1063/1.4771657] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Synthetic nanoscale complexes capable of mechanical movement are often studied theoretically using discrete-state models that involve instantaneous transitions between metastable states. A number of general results have been derived within this framework, including a "no-pumping theorem" that restricts the possibility of generating directed motion by the periodic variation of external parameters. Motivated by recent experiments using time-resolved vibrational spectroscopy [Panman et al., Science 328, 1255 (2010)], we introduce a more detailed and realistic class of models in which transitions between metastable states occur by finite-time, diffusive processes rather than sudden jumps. We show that the no-pumping theorem remains valid within this framework.
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Affiliation(s)
- Dibyendu Mandal
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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Ren J, Liu S, Li B. Geometric heat flux for classical thermal transport in interacting open systems. PHYSICAL REVIEW LETTERS 2012; 108:210603. [PMID: 23003231 DOI: 10.1103/physrevlett.108.210603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2011] [Indexed: 06/01/2023]
Abstract
We study classical heat conduction in a dissipative open system composed of interacting oscillators. By exactly solving a twisted Fokker-Planck equation which describes the full counting statistics of heat flux flowing through the system, we identify the geometric-phase-like effect and examine its impact on the classical heat transport. We find that the nonlinear interaction as well as the closely related temperature dependence of system parameters are crucial in manifesting the geometric-phase contribution of heat flux. Finally, we propose an electronic experiment based on RC circuits to verify our theoretical predictions.
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Affiliation(s)
- Jie Ren
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore.
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Chernyak VY, Klein JR, Sinitsyn NA. Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents. J Chem Phys 2012; 136:154107. [DOI: 10.1063/1.3703328] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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47
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Sagawa T, Ueda M. Nonequilibrium thermodynamics of feedback control. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021104. [PMID: 22463150 DOI: 10.1103/physreve.85.021104] [Citation(s) in RCA: 85] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2011] [Revised: 12/13/2011] [Indexed: 05/10/2023]
Abstract
We establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality in the presence of feedback control with multiple measurements. Our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths. The obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control. A generalized Szilard engine and a feedback-controlled ratchet are shown to satisfy the derived equalities.
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Akimov AV, Sinitsyn NA. Sensitivity field for nonautonomous molecular rotors. J Chem Phys 2011; 135:224104. [DOI: 10.1063/1.3667196] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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50
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Sagawa T, Hayakawa H. Geometrical expression of excess entropy production. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051110. [PMID: 22181372 DOI: 10.1103/physreve.84.051110] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2011] [Revised: 10/24/2011] [Indexed: 05/31/2023]
Abstract
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states.
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Affiliation(s)
- Takahiro Sagawa
- The Hakubi Center, The Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto, Japan
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