Thermodynamic correlation inequalities for finite times and transients

Cai Dieball; Aljaž Godec

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arXiv · 2503.10599

Thermodynamic correlation inequalities for finite times and transients

Cai Dieball·Aljaž Godec

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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.

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Cai Dieball, Aljaž Godec. 2025-03-13. Thermodynamic correlation inequalities for finite times and transients. https://arxiv.org/abs/2503.10599

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