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DY: Fachverband Dynamik und Statistische Physik

DY 44: Poster Session: Statistical Physics and Critical Phenomena

DY 44.2: Poster

Thursday, September 8, 2022, 15:00–18:00, P2

Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes — •Benjamin Ertel, Jann van der Meer, and Udo Seifert — II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany

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 [1].

[1] Benjamin Ertel, Jann van der Meer and Udo Seifert, Phys. Rev. E 105, 044113 (2022)