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

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

2011-08-04

arxiv.org/abs/1108.1135v2

J. Stat. Mech. P10025 (2011)

Physics

Condensed Matter

Statistical Mechanics

25 pages, 4 figures

Scientific paper

10.1088/1742-5468/2011/10/P10025

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.

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