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A large deviation perspective on ratio observables in reset processes: robustness of rate functions. (English) Zbl 1437.60016
Summary: 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.

##### MSC:
 60F10 Large deviations 82B26 Phase transitions (general) in equilibrium statistical mechanics 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
##### Keywords:
large deviations; reset processes; contraction principle
zoverw
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