Arbitrary-time thermodynamic uncertainty relation from fluctuation theorem

The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of the fluctuation of the charge transfer, for example, for a class of continuous-time stochastic processes. However, its extension to general nonequilibrium dynamics is still an unsolved problem. We derive TUR for an arbitrary finite time from exchange fluctuation theorem under a geometric necessary and sufficient condition. We also generally show a necessary and sufficient condition of multidimensional TUR in a unified manner. As a nontrivial practical consequence, we obtain universal scaling relations among the mean and variance of the charge transfer in short time regime. In this manner, we can deepen our understanding of a link between two important rigorous relations, i.e., the fluctuation theorem and the thermodynamic uncertainty relation.

Automated summary

The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of charge transfer fluctuations in continuous-time stochastic processes. However, extending TUR to general nonequilibrium dynamics remains an unsolved problem. In this study, we derive TUR for arbitrary finite time intervals and present a necessary and sufficient condition for multidimensional TUR. We also discover universal scaling relations between the mean and variance of charge transfer in the short time regime, deepening our understanding of the connection between the fluctuation theorem and the thermodynamic uncertainty relation.