Large deviation principles and fluctuation theorems for currents in semi-Markov processes

Faggionato, Alessandra

doi:10.48550/arxiv.1709.05653

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…Generalisation of the level-2.5 and optimal control approaches are also being explored in that context [130]. Another direction of interest is non-Markovian models [47,48,131,132], which can be even richer than the Markovian cases considered here [73,133]. Overall, the field has many interesting open questions, and new methods are becoming available, in order to address them.…”

Section: Discussionmentioning

confidence: 99%

Ergodicity and large deviations in physical systems with stochastic dynamics

2020

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In ergodic physical systems, time-averaged quantities converge (for large times) to their ensembleaveraged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble averages. It allows estimation of the probabilities of these events, and their mechanisms. This theory has been applied to a range of physical systems, where it has yielded new insights into entropy production, current fluctuations, metastability, transport processes, and glassy behaviour. We review some of these developments, identifying general principles. We discuss a selection of dynamical phase transitions, and we highlight some connections between large-deviation theory and optimal control theory. arXiv:1910.09883v1 [cond-mat.stat-mech]

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Section: Discussionmentioning

confidence: 99%

Ergodicity and large deviations in physical systems with stochastic dynamics

2020

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“…The framework of semi-Markov processes [23,32,[81][82][83][84] allows to write the large deviations properties of empirical intervals as follows. The probability to see the empirical density n[τ ; y(1 s τ − 1)] of excursions between resets and the total density n follows the large deviation form…”

Section: Large Deviations For the Empirical Density Of Excursions Bet...mentioning

confidence: 99%

Large deviations for Markov processes with stochastic resetting: analysis via the empirical density and flows or via excursions between resets

Monthus¹

2021

J. Stat. Mech.

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Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at level 2.5 for the joint probability of the empirical density and the empirical flows, or via the large deviations of semi-Markov processes for the empirical density of excursions between consecutive resets. The large deviations properties of general time-additive observables involving the position and the increments of the dynamical trajectory are then analyzed in terms of the appropriate Markov tilted processes and of the corresponding conditioned processes obtained via the generalization of Doob’s h-transform. This general formalism is described in detail for the three possible frameworks, namely discrete-time/discrete-space Markov chains, continuous-time/discrete-space Markov jump processes and continuous-time/continuous-space diffusion processes, and is illustrated with explicit results for the Sisyphus random walk and its variants, when the reset probabilities or reset rates are space-dependent.

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“…In equation (D10), one recognizes the standard form of the rate function for semi-Markov processes [36,38,39,[101][102][103][104][105]. The physical meaning in terms of the alternate excursions on the right and on the left of the origin x = 0 can be understood as follows:…”

Section: J Stat Mech (2021) 083212mentioning

confidence: 99%

Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates

Monthus¹

2021

J. Stat. Mech.

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One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady states when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the large deviations at level 2.5 for the joint probability of the empirical densities, of the empirical spatial currents and of the empirical switching flows. Level 2 for the empirical densities alone can be then derived via the optimization of level 2.5 over the empirical flows. More generally, the large deviations of any time-additive observable can be also obtained via contraction from level 2.5, or equivalently via the deformed generator method and the corresponding Doob conditioned process. Finally, the large deviations for the empirical intervals between consecutive switching events can be obtained via the introduction of the alternate Markov chain that governs the series of all of the switching events of a long trajectory.

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Large deviation principles and fluctuation theorems for currents in semi-Markov processes

Cited by 5 publications

References 12 publications

Ergodicity and large deviations in physical systems with stochastic dynamics

Ergodicity and large deviations in physical systems with stochastic dynamics

Large deviations for Markov processes with stochastic resetting: analysis via the empirical density and flows or via excursions between resets

Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates

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