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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2011

Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain

Résumé

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 for deriving modified fluctuation-dissipation theorems near non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103 090601) 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 the MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a Brownian particle in a harmonic trap subjected 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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Dates et versions

hal-00915481 , version 1 (08-12-2013)

Identifiants

  • HAL Id : hal-00915481 , version 1

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Gatien Verley, Raphael Chetrite, D. Lacoste. Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain. Journal of Statistical Mechanics: Theory and Experiment, 2011, pp.P10025. ⟨hal-00915481⟩
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