Universal Thermodynamic Uncertainty Relation in Non-Equilibrium Dynamics

TL;DR

This paper introduces a universal thermodynamic uncertainty relation applicable to any observable in non-equilibrium Markovian systems, unifying physical and financial inequalities and highlighting the roles of entropy production and non-stationarity.

Contribution

It derives a general TUR that unifies physical and financial inequalities and emphasizes the importance of entropy production and non-stationarity in non-equilibrium systems.

Findings

Both entropy production and non-stationarity are needed to bound thermodynamic currents.

The TUR framework unifies physical and financial inequalities.

The relation applies to arbitrary observables in Markovian systems.

Abstract

We derive a universal thermodynamic uncertainty relation (TUR) that applies to an arbitrary observable in a general Markovian system. The generality of our result allows us to make two findings: (1) for an arbitrary out-of-equilibrium system, both the entropy production and the \textit{degree of non-stationarity} are required to tightly bound the strength of a thermodynamic current; (2) by removing the antisymmetric constraint on observables, the TUR in physics and a fundamental inequality in theoretical finance can be unified in a single framework.