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Farina D, Benazout B, Centrone F, Acín A. Thermodynamic precision in the nonequilibrium exchange scenario. Phys Rev E 2024; 109:034112. [PMID: 38632747 DOI: 10.1103/physreve.109.034112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 01/22/2024] [Indexed: 04/19/2024]
Abstract
We discuss exchange scenario thermodynamic uncertainty relations for the work done on a two-qubit entangled nonequilibrium steady state obtained by coupling the two qubits and putting each of them in weak contact with a thermal bath. In this way we investigate the use of entangled nonequilibrium steady states as end points of thermodynamic cycles. In this framework we prove analytically that for a paradigmatic unitary it is possible to construct an exchange scenario thermodynamic uncertainty relation. However, despite holding in many cases, we also show that such a relation ceases to be valid when considering other suitable unitary quenches. Furthermore, this paradigmatic example allows us to shed light on the role of the entanglement between the two qubits for precise work absorption. By considering the projection of the entangled steady state onto the set of separable states, we provide examples where such projection implies an increase of the relative uncertainty, showing the usefulness of entanglement.
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Affiliation(s)
- Donato Farina
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- Physics Department E. Pancini, Università degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Naples, Italy
| | - Bilal Benazout
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- Physics Department, Ecole Normale Supérieure, Université PSL, 24 rue Lhomond 75005 Paris, France
| | - Federico Centrone
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
| | - Antonio Acín
- ICFO, Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain
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2
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López-Alamilla NJ, Cachi RUL. Virial-like thermodynamic uncertainty relation in the tight-binding regime. CHAOS (WOODBURY, N.Y.) 2022; 32:103109. [PMID: 36319277 DOI: 10.1063/5.0107554] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 09/15/2022] [Indexed: 06/16/2023]
Abstract
We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we provided a tighter lower limit solely in terms of the drift velocity and diffusion. The approach presented is systematically analyzed in the tight-binding regime. We also provide a relative simple rule to validate using the tight-binding approach based on drift and diffusion relations rather than energy barriers and forces. We also discuss the implications of our results outside the tight-binding regime.
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Affiliation(s)
- N J López-Alamilla
- Department of Physics, University of Otago, P. O. Box 56, Dunedin 9054, New Zealand
| | - R U L Cachi
- Department of Chemistry, KU Leuven, Leuven 3001, Belgium
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3
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Paneru G, Dutta S, Pak HK. Colossal Power Extraction from Active Cyclic Brownian Information Engines. J Phys Chem Lett 2022; 13:6912-6918. [PMID: 35866740 PMCID: PMC9358709 DOI: 10.1021/acs.jpclett.2c01736] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
Brownian information engines can extract work from thermal fluctuations by utilizing information. To date, the studies on Brownian information engines consider the system in a thermal bath; however, many processes in nature occur in a nonequilibrium setting, such as the suspensions of self-propelled microorganisms or cellular environments called an active bath. Here, we introduce an archetypal model for a Maxwell-demon type cyclic Brownian information engine operating in a Gaussian correlated active bath capable of extracting more work than its thermal counterpart. We obtain a general integral fluctuation theorem for the active engine that includes additional mutual information gained from the active bath with a unique effective temperature. This effective description modifies the generalized second law and provides a new upper bound for the extracted work. Unlike the passive information engine operating in a thermal bath, the active information engine extracts colossal power that peaks at the finite cycle period. Our study provides fundamental insights into the design and functioning of synthetic and biological submicrometer motors in active baths under measurement and feedback control.
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Affiliation(s)
- Govind Paneru
- Center
for Soft and Living Matter, Institute for
Basic Science (IBS), Ulsan 44919, Republic of Korea
- Department
of Physics, Ulsan National Institute of
Science and Technology, Ulsan 44919, Republic of Korea
| | - Sandipan Dutta
- Department
of Physics, Birla Institute of Technology
and Science, Pilani 333031, India
| | - Hyuk Kyu Pak
- Center
for Soft and Living Matter, Institute for
Basic Science (IBS), Ulsan 44919, Republic of Korea
- Department
of Physics, Ulsan National Institute of
Science and Technology, Ulsan 44919, Republic of Korea
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4
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Lin W, Liao YH, Lai PY, Jun Y. Stochastic currents and efficiency in an autonomous heat engine. Phys Rev E 2022; 106:L022106. [PMID: 36109984 DOI: 10.1103/physreve.106.l022106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 08/10/2022] [Indexed: 06/15/2023]
Abstract
We experimentally demonstrate that a Brownian gyrator of a colloidal particle confined in a two-dimensional harmonic potential with different effective temperatures on orthogonal axes can work as an autonomous heat engine capable of extracting work from the heat bath, generated by an optical feedback trap. The results confirm the theoretically predicted thermodynamic currents and validate the attainability of Carnot efficiency as well as the trade-off relation between power and efficiency. We further show that current fluctuations and the entropy production rate are time independent in the steady state and their product near the Carnot efficiency is close to the lower bound of the thermodynamic uncertainty relation.
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Affiliation(s)
- Wenqi Lin
- Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
| | - Yi-Hung Liao
- Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
| | - Pik-Yin Lai
- Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
| | - Yonggun Jun
- Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
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5
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López-Alamilla NJ, Cachi RUL. A model of minimal entropy generation for cytoskeletal transport systems with multiple interacting motors. Biophys Chem 2022; 288:106853. [PMID: 35753181 DOI: 10.1016/j.bpc.2022.106853] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 05/29/2022] [Accepted: 06/11/2022] [Indexed: 11/30/2022]
Abstract
We study the steady-state rate of entropy generation for multiple interacting particles. The description used is based on the partially asymmetric exclusion process in a lattice with periodic boundary conditions. Our methodology shows that in the steady-state, the rate of entropy generation is directly proportional to the bulk drift and the applied driving force. Since in many cases the driving force is unknown or hard to determine. We circumvent this by deriving a lower bound for the entropy, resulting in an extended thermodynamic uncertainty relation for the asymmetric simple exclusion process. We systematically compared this bound with the actual entropy generation. Thus, we identify the force regimes, and particles' density conditions where the entropy bound derived from this extended thermodynamic uncertainty relation is meaningful.
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Affiliation(s)
| | - R U L Cachi
- Department of Physics, University of Otago, Dunedin, New Zealand; Department of Chemistry, KU Leuven, Leuven, Belgium
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6
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Paneru G, Park JT, Pak HK. Transport and Diffusion Enhancement in Experimentally Realized Non-Gaussian Correlated Ratchets. J Phys Chem Lett 2021; 12:11078-11084. [PMID: 34748337 DOI: 10.1021/acs.jpclett.1c03037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Living cells are known to generate non-Gaussian active fluctuations significantly larger than thermal fluctuations owing to various active processes. Understanding the effect of these active fluctuations on various physicochemical processes, such as the transport of molecular motors, is a fundamental problem in nonequilibrium physics. Therefore, we experimentally and numerically studied an active Brownian ratchet comprising a colloidal particle in an optically generated asymmetric periodic potential driven by non-Gaussian noise having finite-amplitude active bursts, each arriving at random and decaying exponentially. We find that the particle velocity is maximum for relatively sparse bursts with finite correlation time and non-Gaussian distribution. These occasional kicks, which produce Brownian yet non-Gaussian diffusion, are more efficient for transport and diffusion enhancement of the particle than the incessant kicks of active Ornstein-Uhlenbeck noise.
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Affiliation(s)
- Govind Paneru
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Jin Tae Park
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
| | - Hyuk Kyu Pak
- Center for Soft and Living Matter, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
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7
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Kalaee AAS, Wacker A, Potts PP. Violating the thermodynamic uncertainty relation in the three-level maser. Phys Rev E 2021; 104:L012103. [PMID: 34412265 DOI: 10.1103/physreve.104.l012103] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2021] [Accepted: 06/29/2021] [Indexed: 12/15/2022]
Abstract
Nanoscale heat engines are subject to large fluctuations which affect their precision. The thermodynamic uncertainty relation (TUR) provides a trade-off between output power, fluctuations, and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This Letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil-Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres to a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model are not uncommon.
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Affiliation(s)
| | - Andreas Wacker
- Mathematical Physics and NanoLund, Lund University, Box 118, 221 00 Lund, Sweden
| | - Patrick P Potts
- Mathematical Physics and NanoLund, Lund University, Box 118, 221 00 Lund, Sweden.,Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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Saryal S, Sadekar O, Agarwalla BK. Thermodynamic uncertainty relation for energy transport in a transient regime: A model study. Phys Rev E 2021; 103:022141. [PMID: 33736118 DOI: 10.1103/physreve.103.022141] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
We investigate a transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits, and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in the TUR. Interestingly, for all these models, depending on the statistics, the TUR ratio can be expressed as a sum or a difference of a universal term which is always greater than or equal to 2 and a corresponding entropy production term. We find that the generalized version of the TUR, originating from the universal fluctuation symmetry, is always satisfied. However, interestingly, the specialized TUR, a tighter bound, is always satisfied for the coupled harmonic oscillator system obeying Bose-Einstein statistics. Whereas, for both the coupled qubit, obeying Fermi-like statistics, and the hybrid qubit-oscillator system with mixed Fermi-Bose statistics, violation of the tighter bound is observed in certain parameter regimes. We have provided conditions for such violations. We also provide a rigorous proof following the nonequilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems.
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Affiliation(s)
- Sushant Saryal
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Onkar Sadekar
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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9
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Liu K, Gong Z, Ueda M. Thermodynamic Uncertainty Relation for Arbitrary Initial States. PHYSICAL REVIEW LETTERS 2020; 125:140602. [PMID: 33064524 DOI: 10.1103/physrevlett.125.140602] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2019] [Revised: 08/03/2020] [Accepted: 09/09/2020] [Indexed: 05/10/2023]
Abstract
The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs presuppose either specific initial states or an infinite-time average, which severely limits the range of applicability. Here we derive a finite-time TUR valid for arbitrary initial states from the Cramér-Rao inequality. We find that the variance of an accumulated current is bounded from below by the instantaneous current at the final time, which suggests that "the boundary is constrained by the bulk". We apply our results to feedback-controlled processes and successfully explain a recent experiment which reports a violation of a modified TUR with feedback control. We also derive a TUR that is linear in the total entropy production and valid for discrete-time Markov chains with nonsteady initial states. The obtained bound exponentially improves the existing bounds in a discrete-time regime.
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Affiliation(s)
- Kangqiao Liu
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Zongping Gong
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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