Inequalities generalizing the second law of thermodynamics for transitions between non-stationary states

We discuss the consequences of a variant of the Hatano-Sasa relation in which a non-stationary distribution is used in place of the usual stationary one. We first show that this non-stationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and non-adiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law like inequalities for transitions between non-stationary states.Comment: 4 pages, 2 figure

The Metastable Mpemba Effect Corresponds to a Non-monotonic Temperature Dependence of Extractable Work

The Mpemba effect refers to systems whose thermal relaxation time is a non-monotonic function of the initial temperature. Thus, a system that is initially hot cools to a bath temperature more quickly than the same system, initially warm. In the special case where the system dynamics can be described by a double-well potential with metastable and stable states, dynamics occurs in two stages: a fast relaxation to local equilibrium followed by a slow equilibration of populations in each coarse-grained state. We have recently observed the Mpemba effect experimentally in such a setting, for a colloidal particle immersed in water. Here, we show that this metastable Mpemba effect arises from a non-monotonic temperature dependence of the maximum amount of work that can be extracted from the local-equilibrium state at the end of Stage 1

GAMMA CONVERGENCE APPROACH FOR THE LARGE DEVIATIONS OF THE DENSITY IN SYSTEMS OF INTERACTING DIFFUSION PROCESSES

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow variable from the time scale of the fast variable. Its atypical behavior is encapsulated in a large N Large Deviation Principle (LDP) with a rate functional. We study the Γ-convergence of as → 0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory (MFT) for diffusive systems

Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying markovian dynamics. We show that the method to derive modified fluctuation-dissipation theorems near non-equilibrium stationary states used by J. Prost et al., PRL 103, 090601 (2009), is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano-Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy, in a way which is similar to what has been done recently in the case of MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a brownian particle in an harmonic trap submitted to a quench of temperature and to a time-dependent stiffness. The second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics.Comment: 25 pages, 4 figure

A fresh understanding of the Mpemba effect

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Inequalities generalizing the second law of thermodynamics for transitions between non-stationary states

We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and nonadiabatic entropies introduced by M. Esposito and C. Van Introduction.-The second law of thermodynamics provides fundamental limitations on the way transitions between equilibrium states can occur. For many years, this principle could only be expressed as an inequality. A broad number of works summarized under the name of fluctuations theorems In these generalizations, an essential step was made by Hatano and Sas

Erratum: Martingale theory for housekeeping heat

Original article: EPL, 124 (2018) 6000