Thermodynamic theory for history-dependent intensities

Develop the thermodynamic framework for history-dependent transition intensities, including local detailed balance, entropy production, and corresponding uncertainty relations, in general non-Markovian jump dynamics.

Background

The paper develops kinetic fluctuation-response relations and activity-controlled response-kinetic uncertainty relations for causal, history-dependent jump processes without assuming Markovianity or a thermodynamic interpretation of the event channels. It notes that extending these results to thermodynamic quantities requires specifying how history-dependent rates satisfy local detailed balance and how entropy production should be defined.

The unresolved problem is to establish this thermodynamic structure in general and connect it to existing semi-Markov thermodynamics and associated uncertainty relations. This would provide a thermodynamic interpretation of the trajectory-level response bounds developed in the paper.

References

The thermodynamic content of history-dependent intensities---local detailed balance, entropy production, and their uncertainty relations---connects the present kinetic bounds to semi-Markov thermodynamics and remains to be developed in general.

— The Memory Hidden in Response Fluctuations: Trajectory-Level Fluctuation-Response Theory and Inequalities for Non-Markovian Jump Dynamics  (2608.20328 - Zheng et al., 20 Aug 2026) in Section 10, “Discussions and outlooks”