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Maes, Christian; Netočný, Karel

doi:10.1023/a:1021026930129

Cited by 250 publications

(243 citation statements)

References 19 publications

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“…Another consequence of microreversibility are the so-called fluctuation theorems, which characterize the large fluctuations of physical quantities in nonequilibrium systems. They have been derived in deterministic [3,4,5,6] or Markovian stochastic systems [7,8,9,10] and concern different quantities such as the entropy production [5], the dissipated work [11,12], or the currents crossing the system in a nonequilibrium situation [13,14,15]. Such relations are important because they are valid far from equilibrium.…”

Section: Introductionmentioning

confidence: 99%

A fluctuation theorem for currents and non-linear response coefficients

2007

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We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations.

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Section: Introductionmentioning

confidence: 99%

A fluctuation theorem for currents and non-linear response coefficients

2007

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“…Regarding this difficulty, neither a proof of the non-decreasing property of S(C t ) nor a counter example is obtained, whereas S (0) (C t ) is found to be non-decreasing when the Navier-Stokes equation is considered. The understanding of S(C) beyond S (0) (C) may be connected to steadystate thermodynamics [37][38][39][40][41][42][43][44][45][46].…”

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confidence: 99%

Derivation of Hydrodynamics from the Hamiltonian Description of Particle Systems

Sasa

2014

Phys. Rev. Lett.

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Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation.

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“…For instance, in the recent work [19], Maes and Netocny considered the topic of a renormalized Clausius inequality in the context of a single Brownian particle in a time dependent environment. To compare the approach in [19] to the present one, consider N independent diffusions in the thermodynamic limit N → ∞. Each diffusion solves the Langevin equationẊ = E(t, X) + √ 2ẇ, where E is a time dependent vector field andẇ denotes white noise.…”

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confidence: 99%

“…Our renormalized work is given by (12) with J A (t, ρ) = ρ E(t, x) + ∇v(t, x) . The renormalization introduced in [19] is instead obtained by introducing a potential field such that the corresponding stationary state has minimal entropy production. Namely, they write E = f − ∇U and subtract from the energy exchanged the space-time integral of |J ϕ t | 2 /ρ where J ϕ t = ρ(f − ∇ϕ) − ∇ρ and ϕ = ϕ(t, x; ρ) is chosen so that ∇ · J ϕ t = 0.…”

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Clausius Inequality and Optimality of Quasistatic Transformations for Nonequilibrium Stationary States

et al. 2013

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Nonequilibrium stationary states of thermodynamic systems dissipate a positive amount of energy per unit of time. If we consider transformations of such states that are realized by letting the driving depend on time, the amount of energy dissipated in an unbounded time window becomes then infinite. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work performed along any given transformation. We then show that the renormalized work satisfies a Clausius inequality and prove that equality is achieved for very slow transformations, that is in the quasi static limit. We finally connect the renormalized work to the quasi potential of the macroscopic fluctuation theory, that gives the probability of fluctuations in the stationary nonequilibrium ensemble. A main goal of nonequilibrium thermodynamics is to construct analogues of thermodynamic potentials for nonequilibrium stationary states. These potentials should describe the typical macroscopic behavior of the system as well as the asymptotic probability of fluctuations. As it has been shown in [1], this program can be implemented without the explicit knowledge of the stationary ensemble and requires as input the macroscopic dynamical behavior of systems which can be characterized by the transport coefficients. This theory, now known as macroscopic fluctuation theory, is based on an extension of Einstein equilibrium fluctuation theory to stationary nonequilibrium states combined with a dynamical point of view. It has been very powerful in studying concrete microscopic models but can be used also as a phenomenological theory. It has led to several new interesting predictions [2][3][4][5][6][7].From a thermodynamic viewpoint, the analysis of transformations from one state to another one is most relevant. This issue has been addressed by several authors in different contexts. For instance, following the basic papers [8][9][10], the case of Hamiltonian systems with finitely many degrees of freedom has been recently discussed in [11,12] while the case of Langevin dynamics is considered in [13].We here consider thermodynamic transformations for driven diffusive systems in the framework of the macroscopic fluctuation theory. With respect to the authors mentioned above, the main difference is that we deal with systems with infinitely many degrees of freedom and the spatial structure becomes relevant. For simplicity of notation, we restrict to the case of a single conservation law, e.g., the conservation of the mass. We thus consider an open system in contact with boundary reservoirs, characterized by their chemical potential λ, and under the action of an external field E. We denote by Λ ⊂ R d the bounded region occupied by the system, by x the macroscopic space coordinates and by t the macroscopic time. With respect to our previous work [1, 3, 4], we here consider the case in which λ and E depend explicitly on the time t, driving the system from a nonequilibrium state to...

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Cited by 250 publications

References 19 publications

A fluctuation theorem for currents and non-linear response coefficients

A fluctuation theorem for currents and non-linear response coefficients

Derivation of Hydrodynamics from the Hamiltonian Description of Particle Systems

Clausius Inequality and Optimality of Quasistatic Transformations for Nonequilibrium Stationary States

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