Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes

Abstract

Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium imposes a crucial condition called direction-time independence for which we present an alternative derivation. We prove a thermodynamic uncertainty relation that formally resembles the one for a discrete-time Markov process. The result relates the entropy production of the semi-Markov process to mean and variance of steady-state currents. We prove a further thermodynamic uncertainty relation valid for semi-Markov descriptions of coarse-grained Markov processes that emerge by grouping states together. A violation of this inequality can be used as an inference tool to conclude that a given semi-Markov process cannot result from coarse-graining an underlying Markov one. We illustrate these results with representative examples.

References in corpus (23)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Anomalous transport in the crowded world of biological cells
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Random walks and diffusion on networks
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Fluctuation theorem for currents and Schnakenberg network theory
• Discrete-time thermodynamic uncertainty relation
• Thermodynamic uncertainty relation for time-dependent driving
• Multidimensional thermodynamic uncertainty relations
• Uncertainty relations in stochastic processes: An information inequality approach
• Inferring broken detailed balance in the absence of observable currents
• The inspection paradox in stochastic resetting
• The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook
• Entropy production and coarse-graining in Markov processes
• Emergent memory and kinetic hysteresis in strongly driven networks
• Continuous time random walk for open systems: Fluctuation theorems and counting statistics
• Exact Coarse Graining Preserves Entropy Production out of Equilibrium
• Semi-Markov approach to continuous time random walk limit processes
• Dynamical fluctuations for semi-Markov processes
• Affinity- and topology-dependent bound on current fluctuations
• Optimal thermodynamic uncertainty relation in Markov jump processes

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