Thermodynamic formalism and large deviation functions in continuous time Markov dynamics

Details Thermodynamic formalism and large deviation functions in continuous time Markov dynamics Thermodynamic formalism and large deviation functions in continuous time Markov dynamics

2007-03-16

arxiv.org/abs/cond-mat/0703435v1

Comptes Rendus Physique 8 (2007) 609-619

Physics

Condensed Matter

Statistical Mechanics

Proceedings of the conference "Work, dissipation, and fluctuations in nonequilibrium physics" held in Brussels 22-25 March 200

Scientific paper

10.1016/j.crhy.2007.05.005

The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted in an appropriate way. Besides, it can be reformulated in terms of the generating function of an observable, and then extended to other observables. In particular, the simple observable $K$ giving the number of events occurring over a given time interval turns out to contain already the signature of dynamical phase transitions. For mean-field models in equilibrium, and in the limit of large systems, the formalism is rather simple to apply and shows how thermodynamic phase transitions may modify the dynamical properties of the systems. This is exemplified with the q-state mean-field Potts model, for which the Ising limit q=2 is found to be qualitatively different from the other cases.

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