An integral fluctuation theorem for systems with unidirectional transitions

Abstract

The fluctuations of a Markovian jump process with one or more unidirectional transitions, where $R_{ij}>0$ but $R_{ji}=0$, are studied. We find that such systems satisfy an integral fluctuation theorem. The fluctuating quantity satisfying the theorem is a sum of the entropy produced in the bidirectional transitions and a dynamical contribution which depends on the residence times in the states connected by the unidirectional transitions. The convergence of the integral fluctuation theorem is studied numerically, and found to show the same qualitative features as in systems exhibiting microreversibility.

14 pages, 3 figures

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• Fluctuation theorems for stochastic dynamics
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• Entropic bounds on currents in Langevin systems
• Integral Fluctuation Theorems for Stochastic Resetting Systems
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• Entropy production in systems with unidirectional transitions
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Tighter thermodynamic bound on speed limit in systems with unidirectional transitions
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Inflow rate, a time-symmetric observable obeying fluctuation relations
• Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting