Thermodynamic correlation inequalities for finite times and transients

TL;DR

This work extends thermodynamic correlation inequalities from infinite-time steady-state settings to finite observation times and transient dynamics in overdamped Langevin systems. It derives finite-time bounds that relate the variance of time-averaged observables to short-time dissipation and entropy production, using stochastic calculus and spectral decompositions, and it generalizes to complex-valued observables. The authors also establish transient bounds for dynamics approaching DB or NESS through a Σ-weighted framework and introduce a pseudo-variance to handle transients. The work opens routes for inferring entropy production from finite-time correlation decay and suggests practical applications in experiments and extensions to more general dynamics.

Abstract

Recently, a thermodynamic bound on correlation times was formulated in [A. Dechant, J. Garnier-Brun, S.-i. Sasa, Phys. Rev. Lett. 131, 167101 (2023)], showing how the decay of correlations in Langevin dynamics is bounded by short-time fluctuations and dissipation. Whereas these original results only address very long observation times in steady-state dynamics, we here generalize the respective inequalities to finite observations and general initial conditions. We utilize the connection between correlations and the fluctuations of time-integrated density functionals and generalize the direct stochastic calculus approach from [C. Dieball and A. Godec, Phys. Rev. Lett. 130, 087101 (2023)] which paves the way for further generalizations. We address the connection between short and long time scales, as well as the saturation of the bounds via complementary spectral-theoretic arguments. Motivated by the spectral insight, we formulate all results also for complex-valued observables.