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  Direct Route to Thermodynamic Uncertainty Relations and Their Saturation

Dieball, C., & Godec, A. (2023). Direct Route to Thermodynamic Uncertainty Relations and Their Saturation. arXiv. doi:10.48550/arXiv.2208.06402.

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Dieball, Cai1, Author           
Godec, Aljaz1, Author           
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1Research Group of Mathematical Biophysics, Max Planck Institute for Multidisciplinary Sciences, Max Planck Society, ou_3350133              

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 Abstract: Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. In addition, we extend the transient TUR to currents and densities with explicit time-dependence. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most direct proof, together with the new generalizations, allows us to systematically determine conditions under which the different TURs saturate and thus allows for a more accurate thermodynamic inference. Finally we outline the direct proof also for Markov jump dynamics.

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Language(s): eng - English
 Dates: 2023-01-13
 Publication Status: Published online
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 Rev. Type: No review
 Identifiers: DOI: 10.48550/arXiv.2208.06402
arXiv: 2208.06402v4
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