Entropy production in irreversible systems described by a Fokker-Planck equation

Tomé, Tânia; Oliveira, Mário J. de

doi:10.1103/physreve.82.021120

Cited by 135 publications

(210 citation statements)

References 33 publications

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“…It would be interesting to compare systematically this approach with the one based on a statistical definition of entropy in terms of probability distributions of the state variables, such as the Gibbs-Shannon form used in [11,18,19]. In this approach, entropy production is defined in terms of the probability fluxes appearing in the Fokker-Planck equation corresponding to the Langevin dynamics (55).…”

Section: Discussionmentioning

confidence: 99%

“…The first term in the last equality, to which we will refer as the systematic part, has exactly the same structure as the deterministic entropy production (18) and is consequently always non-negative, despite the fact that v is now a stochastic variable. The second term (the fluctuating part) contains a contribution in which the random force appears explicitly and is thus not necessarily positive at all times and positions.…”

Section: Stochastic Thermodynamics: Extended Local Equilibrium Approachmentioning

confidence: 99%

“…Considerable effort has been made to identify thermodynamic quantities like work, heat or entropy at the level of a single Brownian particle [6,11,[14][15][16][17]. On the other hand, much less attention has been paid to the stochastic thermodynamics of a collection (a binary solution) of Brownian particles embedded in a fluid [11,18,19]. One of our aims is to establish the fluctuating thermodynamics of such a system, which is much closer to the type of systems considered in classical irreversible thermodynamics, and to assess the role of collective effects in the thermodynamic properties.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Thermodynamics of Brownian Motion

Nicolis

Decker

2017

Entropy

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A stochastic thermodynamics of Brownian motion is set up in which state functions are expressed in terms of state variables through the same relations as in classical irreversible thermodynamics, with the difference that the state variables are now random fields accounting for the effect of fluctuations. Explicit expressions for the stochastic analog of entropy production and related quantities are derived for a dilute solution of Brownian particles in a fluid of light particles. Their statistical properties are analyzed and, in the light of the insights afforded, the thermodynamics of a single Brownian particle is revisited and the status of the second law of thermodynamics is discussed.

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Section: Discussionmentioning

confidence: 99%

Section: Stochastic Thermodynamics: Extended Local Equilibrium Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Thermodynamics of Brownian Motion

Nicolis

Decker

2017

Entropy

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“…[9], but generalise it in two ways. First, it includes systems with arbitrary combinations of even and odd variables and second, it includes non-diagonal D's.…”

Section: Entropy Production: General Statementmentioning

confidence: 99%

“…For instance, by comparing forward and backward experiments, it enables one to the relate the entropy production directly to the stochastic trajectories of the system [2][3][4][5]. When describing a non-equilibrium system in terms of stochastic processes, much of the focus has naturally been on Markovian dynamics, in particular using the master equation [2,3,[6][7][8] or the Fokker-Planck approach [4,9,10], which will be the choice for the present paper. We also note that non-Markovian dynamics have also been recently investigated [11].…”

Section: Introductionmentioning

confidence: 99%

Entropy production in linear Langevin systems

Landi¹,

Tomé²,

Oliveira³

2013

J. Phys. A: Math. Theor.

Self Cite

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We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem.

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Characterizing Irreversibility in Open Quantum Systems

Batalhão

Gherardini

Santos

et al. 2018

Fundamental Theories of Physics

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Irreversibility is a fundamental concept with important implications at many levels. It pinpoints the fundamental difference between the intrinsically reversible microscopic equations of motion and the unidirectional arrow of time that emerges at the macroscopic level. More pragmatically, a full quantification of the degree of irreversibility of a given process can help in the characterisation of the performance of thermo-machines operating at the quantum level. Here, we review the concept of entropy production, which is commonly intended as the measure of thermodynamic irreversibility of a process, pinpointing the features and shortcomings of its current formulation.When watching a movie, a question that can be made is whether the movie was recorded in that way, or if we are watching a time-reversed version of the actual recording. In our everyday experience, this question is often easy to answer, because watching broken pieces of glass moving from the floor to the top of a table and assembling themselves in the shape of a cup just feels weird. It is much more likely that the movie-makers recorded a glass cup falling down and breaking. Even though we are able to reach this conclusion quickly, none of the fundamental laws of physics (e.g., Newtonian equations of motion) forbid the broken pieces to reassemble the cup. Only the second law of thermodynamics makes the argument that, as the broken pieces represent a system of larger entropy, the reassembling process is impossible or at least very unlikely.The above is only a simple example, taken from everyday life, of a much deeper concept, namely that the fundamental, microscopic equations of motion are symmetric under time-reversal, but the thermodynamical laws are not and establish a fundamental difference between past and future. This apparent paradox has been known under the name of the "arrow of time", given by Eddington in 1927 [1]. The understanding of the emergence of the arrow of time from underlying quantum dynamics, and the formalisation of a self-consistent framework for its characterisation have been the focus of much interest. On one hand, we are in great need of tools able to reveal, experimentally, the implications that nonequilibrium dynamics has on the degree of reversibility for a given quantum process. On the other hand, the tools that are currently available for the (even only theoretical) investigation of thermodynamic irreversibility lack the widespread applicability and logical selfcontained nature that is required from a complete theory. Let us elaborate more on this aspect.The entropy of an open system, unlike the energy, does not satisfy a continuity equation: in addition to entropic fluxes exchanged between a system and its environment, some entropy may also be produced within the system. This contribution is called entropy production and, according to the second law of thermodynamics, it is always non-negative, being zero only when the system and the environment are in thermal equilibrium. On the other hand, for closed systems that are d...

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Entropy production in irreversible systems described by a Fokker-Planck equation

Cited by 135 publications

References 33 publications

Stochastic Thermodynamics of Brownian Motion

Stochastic Thermodynamics of Brownian Motion

Entropy production in linear Langevin systems

Characterizing Irreversibility in Open Quantum Systems

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