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 ($E({\mathcal{C}}^{\prime })-E(\mathcal{C})$).

15 pages

References in corpus (9)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Steady state statistics of driven diffusions
• Large deviations conditioned on large deviations II: Fluctuating hydrodynamics
• Thermodynamic formalism and large deviation functions in continuous time Markov dynamics
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations

Cited by in corpus (22)

• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Jump-Drift and Jump-Diffusion Processes : Large Deviations for the density, the current and the jump-flow and for the excursions between jumps
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• Conditioning diffusion processes with killing rates
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Microcanonical conditioning of Markov processes on time-additive observables
• Markov trajectories : Microcanonical Ensembles based on empirical observables as compared to Canonical Ensembles based on Markov generators
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
• Markov spin models for image generation : explicit large deviations with respect to the number of pixels
• Conditioning two diffusion processes with respect to their first-encounter properties