A large deviation perspective on ratio observables in reset processes: robustness of rate functions

Abstract

We study large deviations of a ratio observable in discrete-time reset processes. The ratio takes the form of a current divided by the number of reset steps and as such it is not extensive in time. A large deviation rate function can be derived for this observable via contraction from the joint probability density function of current and number of reset steps. The ratio rate function is differentiable and we argue that its qualitative shape is 'robust', i.e. it is generic for reset processes regardless of whether they have short- or long-range correlations. We discuss similarities and differences with the rate function of the efficiency in stochastic thermodynamics.

arXiv comment17 pages, 15 figures

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Cited by in corpus (12)

• Stochastic resetting: A (very) brief review
• Stochastic resetting in interacting particle systems: A review
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Controlling particle currents with evaporation and resetting from an interval
• Thermodynamic cost of finite-time stochastic resetting
• Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
• Graph-combinatorial approach for large deviations of Markov chains
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• Manipulating phases in many-body interacting systems with subsystem resetting
• Understanding random-walk dynamical phase coexistence through waiting times
• Density-dependent stochastic resetting: a large deviations framework for achieving target distributions over networks