We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is, if the initial measure ν is invariant for the given Markov semi-group, then for any pair of times s
Publié le : 2010-08-15
Classification:
Markov processes,
Out of equilibrium statistical physics,
Langevin dynamics,
Dirichlet forms,
Fluctuation Dissipation Theorem,
60J25,
82C05,
82C31,
60J75,
60J60,
60K35
@article{1281100400,
author = {Dembo, Amir and Deuschel, Jean-Dominique},
title = {Markovian perturbation, response and fluctuation dissipation theorem},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 822-852},
language = {en},
url = {http://dml.mathdoc.fr/item/1281100400}
}
Dembo, Amir; Deuschel, Jean-Dominique. Markovian perturbation, response and fluctuation dissipation theorem. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 822-852. http://gdmltest.u-ga.fr/item/1281100400/