Operationally accessible uncertainty relations for thermodynamically consistent semi-Markov processes

• Main Authors: Ertel, B. (Author), Seifert, U. (Author), Van Der Meer, J. (Author)
• Format: Article
• Language: English
• Published: American Physical Society 2022
• Subjects: Condition; Discrete time markov process; Entropy; Entropy production; Markov kernels; Markov processes; Memory effects; Semi markov process; Semi-Markov; Temporal memory; Thermodynamic consistency; Uncertainty relation
• Online Access: View Fulltext in Publisher

 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. © 2022 American Physical Society.