Thermodynamic formalism and large deviation functions in continuous time Markov dynamics
arXiv:cond-mat/0703435 · doi:10.1016/j.crhy.2007.05.005
Abstract
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 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.
Proceedings of the conference "Work, dissipation, and fluctuations in nonequilibrium physics" held in Brussels 22-25 March 2006. Submitted to CRAS
References in corpus (4)
Cited by in corpus (36)
- Thermodynamic formalism for systems with Markov dynamics
- Simulating rare events in dynamical processes
- Introduction to dynamical large deviations of Markov processes
- Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
- Computation of current cumulants for small nonequilibrium systems
- Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
- Microscopic Fluctuation Theory (mFT) for interacting Poisson processes
- Large Deviations for the density and the current in Non-Equilibrium-Steady-States on disordered rings
- Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
- Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
- Large Deviations for dynamical fluctuations of Open Markov processes, with application to random cascades on trees
- Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
- Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
- Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs
- 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
- Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
- 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
- A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
- 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
- Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
- Markov trajectories : Microcanonical Ensembles based on empirical observables as compared to Canonical Ensembles based on Markov generators
- Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
- Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
- Conditioning diffusion processes with respect to the local time at the origin
- Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
- 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
- Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
- Large deviations for trajectory observables of diffusion processes in dimension in the double limit of large time and small diffusion coefficient
- A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
- Markov spin models for image generation : explicit large deviations with respect to the number of pixels
- Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
- Conditioning two diffusion processes with respect to their first-encounter properties