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Abstract
We apply the adiabatic approximation to slow but finite-time thermodynamic processes and obtain the full counting statistics of work. The average work consists of change in free energy and the dissipated work, and we identify each term as a dynamical- and geometric-phase-like quantity. An expression for the friction tensor, the key quantity in thermodynamic geometry, is explicitly given. The dynamical and geometric phases are proved to be related to each other via the fluctuation-dissipation relation.
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Affiliation(s)
- Jie Gu
- Chengdu Academy of Education Sciences, Chengdu 610036, China
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2
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Fiore CE, Harunari PE, Noa CEF, Landi GT. Current fluctuations in nonequilibrium discontinuous phase transitions. Phys Rev E 2021; 104:064123. [PMID: 35030860 DOI: 10.1103/physreve.104.064123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Accepted: 11/29/2021] [Indexed: 11/07/2022]
Abstract
Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime-a hallmark of discontinuous transitions-in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the conditional statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of large deviation theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlögl's model of chemical reactions, and a 12-state Potts model subject to two baths at different temperatures.
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Affiliation(s)
- C E Fiore
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Pedro E Harunari
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil.,Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg L-1511, G.D. Luxembourg
| | - C E Fernández Noa
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Gabriel T Landi
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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Forastiere D, Falasco G, Esposito M. Strong current response to slow modulation: A metabolic case-study. J Chem Phys 2020; 152:134101. [PMID: 32268754 DOI: 10.1063/1.5143197] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under time-varying metabolic conditions, modeled by a periodic modulation of the product concentration. We find that the system exhibits a strong nonlinear response to small driving frequencies both for the mean time-averaged current and for the fluctuations. For the first, we obtain an analytic formula by coarse-graining the original model to a solvable one. The result is nonperturbative in the modulation amplitude and frequency. We then refine the picture by studying the stochastic dynamics of the full system using a large deviation approach that allows us to show the resonant effect at the level of the time-averaged variance and signal-to-noise ratio. Finally, we discuss how this nonequilibrium effect may play a role in metabolic and synthetic networks.
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Affiliation(s)
- Danilo Forastiere
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, Luxembourg City L-1511, Luxembourg
| | - Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, Luxembourg City L-1511, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, Luxembourg City L-1511, Luxembourg
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Salazar DSP. Work distribution in thermal processes. Phys Rev E 2020; 101:030101. [PMID: 32289888 DOI: 10.1103/physreve.101.030101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 02/20/2020] [Indexed: 06/11/2023]
Abstract
We find the moment generating function (mgf) of the nonequilibrium work for open systems undergoing a thermal process, i.e., when the stochastic dynamics maps thermal states into time-dependent thermal states. The mgf is given in terms of a temperaturelike scalar satisfying a first-order ordinary differential equation. We apply the result to some paradigmatic situations: a levitated nanoparticle in a breathing optical trap, a Brownian particle in a box with a moving piston, and a two-state system driven by an external field, where the work mgfs are obtained for different timescales and compared with Monte Carlo simulations.
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Affiliation(s)
- Domingos S P Salazar
- Unidade Acadêmica de Educação a Distância e Tecnologia, Universidade Federal Rural de Pernambuco, Recife, Pernambuco 52171-900, Brazil
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Dutta A, Das A, Sengupta K. Statistics of work distribution in periodically driven closed quantum systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012104. [PMID: 26274122 DOI: 10.1103/physreve.92.012104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Indexed: 06/04/2023]
Abstract
We study the statistics of the work distribution P(w) in a d-dimensional closed quantum system with linear dimension L subjected to a periodic drive with frequency ω(0). We show that the corresponding rate function I(w)=-ln[P(w)/Λ(0)]/L^{d} after a drive period satisfies a universal lower bound I(0)≥n(d) and has a zero at w=QL(d)/N, where n(d) and Q are the excitation and the residual energy densities generated during the drive, Λ(0) is a constant fixed by the normalization of P(w), and N is the total number of constituent particles or spins in the system. We supplement our results by calculating I(w) for a class of d-dimensional integrable models and show that I(w) has an oscillatory dependence on ω(0) originating from Stuckelberg interference generated due to double passage through the critical point or region during the drive. We suggest experiments to test our theory.
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Affiliation(s)
- Anirban Dutta
- Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - Arnab Das
- Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | - K Sengupta
- Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Yi SD, Baek SK. Interrupted coarsening in the zero-temperature kinetic Ising chain driven by a periodic external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062107. [PMID: 26172661 DOI: 10.1103/physreve.91.062107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2015] [Indexed: 06/04/2023]
Abstract
If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly oscillating periodic field with enough strength to compete with the spin-spin interaction. By analyzing correlation functions and the distribution of domain lengths both analytically and numerically, we observe nontrivial correlation with more than one length scale at the threshold field strength.
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Affiliation(s)
- Su Do Yi
- Department of Physics, Pukyong National University, Busan 608-737, Korea
| | - Seung Ki Baek
- Department of Physics, Pukyong National University, Busan 608-737, Korea
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Multifractality of random eigenfunctions and generalization of Jarzynski equality. Nat Commun 2015; 6:7010. [PMID: 25912652 PMCID: PMC4421851 DOI: 10.1038/ncomms8010] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2014] [Accepted: 03/24/2015] [Indexed: 11/09/2022] Open
Abstract
Systems driven out of equilibrium experience large fluctuations of the dissipated work. The same is true for wavefunction amplitudes in disordered systems close to the Anderson localization transition. In both cases, the probability distribution function is given by the large-deviation ansatz. Here we exploit the analogy between the statistics of work dissipated in a driven single-electron box and that of random multifractal wavefunction amplitudes, and uncover new relations that generalize the Jarzynski equality. We checked the new relations theoretically using the rate equations for sequential tunnelling of electrons and experimentally by measuring the dissipated work in a driven single-electron box and found a remarkable correspondence. The results represent an important universal feature of the work statistics in systems out of equilibrium and help to understand the nature of the symmetry of multifractal exponents in the theory of Anderson localization. The work fluctuations of systems driven out of equilibrium are governed by the same large-deviation theory as wavefunction amplitudes close to the Anderson localization transition. Exploiting this analogy, the authors generalize the Jarzynski equality, verifying their relation on a single-electron box.
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Verley G, Willaert T, Van den Broeck C, Esposito M. Universal theory of efficiency fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052145. [PMID: 25493777 DOI: 10.1103/physreve.90.052145] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2014] [Indexed: 06/04/2023]
Abstract
Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from equilibrium. In particular, the probabilities for observing the reversible efficiency and the least likely efficiency are identical to those of the same machine working under the time-reversed driving. For time-symmetric drivings, this reversible and the least probable efficiency coincide.
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Affiliation(s)
- Gatien Verley
- Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
| | | | | | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
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Pal A, Sabhapandit S. Work fluctuations for a Brownian particle driven by a correlated external random force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:052116. [PMID: 25493749 DOI: 10.1103/physreve.90.052116] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Indexed: 06/04/2023]
Abstract
We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external force on the Brownian particle in a given time interval in the steady state. We calculate the large deviation functions as well as the complete asymptotic form of the probability density function of the performed work. We also discuss the symmetry properties of the large deviation functions for this system. Finally we perform numerical simulations and they are in a very good agreement with the analytic results.
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Affiliation(s)
- Arnab Pal
- Raman Research Institute, Bangalore 560080, India
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Baek SK, Marchesoni F. Nonequilibrium steady state of the kinetic Glauber-Ising model under an alternating magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022136. [PMID: 25353451 DOI: 10.1103/physreve.89.022136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Indexed: 06/04/2023]
Abstract
When periodically driven by an external magnetic field, a spin system can enter a phase of steady entrained oscillations with nonequilibrium probability distribution function. We consider an arbitrary magnetic field switching its direction with frequency comparable with the spin-flip rate and show that the resulting nonequilibrium probability distribution can be related to the system equilibrium distribution in the presence of a constant magnetic field of the same magnitude. We derive convenient approximate expressions for this exact relation and discuss their implications.
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Affiliation(s)
- Seung Ki Baek
- Department of Physics, Pukyong National University, Busan 608-737, Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
| | - Fabio Marchesoni
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea and Dipartimento di Fisica, Università di Camerino, I-62032 Camerino, Italy
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