Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs

Abstract

For a system in contact with several reservoirs $r$ at different inverse-temperatures ${\beta }_r$, we describe how the Markov jump dynamics with the generalized detailed balance condition can be analyzed via a statistical physics approach of dynamical trajectories $[\mathcal{C}(t){]}_{0\le t\le T}$ over a long time interval $T\to +\infty$. The relevant intensive variables are the time-empirical density $\rho (\mathcal{C})$, that measures the fractions of time spent in the various configurations $\mathcal{C}$, and the time-empirical jump densities $k_r({\mathcal{C}}^{\prime },\mathcal{C})$, that measure the frequencies of jumps from configuration $\mathcal{C}$ to configuration ${\mathcal{C}}^{\prime }$ when it is the reservoir $r$ that furnishes or absorbs the corresponding energy difference ($E({\mathcal{C}}^{\prime })-E(\mathcal{C})$).

arXiv comment15 pages

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