Entropy production in systems with unidirectional transitions

Abstract

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.

arXiv comment(Accepted for publication in Physical Review Research)

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• Stochastic resetting: A (very) brief review
• Stochastic resetting with stochastic returns using external trap
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Random acceleration process under stochastic resetting
• Resetting with stochastic return through linear confining potential
• Coarse-grained entropy production with multiple reservoirs: unraveling the role of time-scales and detailed balance in biology-inspired systems
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events
• Thermodynamic cost of finite-time stochastic resetting
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• Tighter thermodynamic bound on speed limit in systems with unidirectional transitions
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• Stochastic resetting with refractory periods: pathway formulation and exact results
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• Designing Autonomous Maxwell Demon via Stochastic Resetting
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• Emerging cost-time Pareto front for diffusion with stochastic return
• Information thermodynamics of transition paths between multiple mesostates
• Inducing and optimizing Markovian Mpemba effect with stochastic reset