Thermodynamic Formalism for Systems with Markov Dynamics

By V. Lecomte, Cécile Appert-Rolland, F. van Wijland. 2006

282 citations recorded by the source corpus.

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time.We also generalize the formalism—a dynamical Gibbs ensemble construction—to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem.We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3d6c8217183d4de61b235dba3eefb4b5b4787e66

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Nonequilibrium Markov Processes Conditioned on Large Deviations (2014, background): “[78], the so-called activity [65,66,90,91], which is essentially the number of jumps, in addition to work- and heat-related quantities defined for systems in contact with heat reservoirs and driven by external forces [92,93].”
Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, methodology): “ terms of a \transfer matrix". This reduces the problem of calculating a partition sum, to the often simpler problem of maximising an operator. In particular, the MGF, Eq.(22), can be written as [10, 41, 26] Z(s) = hj etW sjP 0i; (28) where P 0 is the initial distribution of congurations. The o”
Kinetically Constrained Models (2010, unknown): “This phase transitions can be studied by recourse to the large-deviation method (Lecomte et al., 2007; Touchette, 2009).”