Thermodynamic formalism and large deviation functions in continuous time Markov dynamics

Thermodynamic Formalism, Large Deviation, and Multifractals

Thermodynamic formalism for countable Markov shifts

We give an overview of the thermodynamic formalism for countable Markov shifts, and indicate applications to surface diffeomorphisms. 1. What is “thermodynamic formalism”? 1.

Thermodynamic Formalism for Random Countable Markov Shifts

We introduce a relative Gurevich pressure for random countable topologically mixing Markov shifts. It is shown that the relative variational principle holds for this notion of pressure. We also prove a relative RuellePerron-Frobenius theorem which enables us to construct a wealth of invariant Gibbs measures for locally fiber Hölder continuous functions. This is accomplished via a new constructi...

The deviation matrix of a continuous-time Markov chain

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P (.) and ergodic matrix Π is the matrix D ≡ ∫∞ 0 (P (t)−Π)dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of deviation matrices by showing that a me...

Nonequilibrium thermodynamic potentials for continuous-time Markov chains.

We connect the rare fluctuations of an equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics an...