Direct Route to Thermodynamic Uncertainty Relations and Their Saturation

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.

arXiv commentFinal version accepted for publication in Physical Review Letters

References in corpus (52)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• How far from equilibrium is active matter?
• The Three Faces of the Second Law: I. Master Equation Formulation
• Nonequilibrium Markov processes conditioned on large deviations
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Universal bounds on current fluctuations
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Estimating dissipation from single stationary trajectories
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Finite-time generalization of the thermodynamic uncertainty relation
• Quantifying dissipation using fluctuating currents
• Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
• Current fluctuations and transport efficiency for general Langevin systems
• Discrete-time thermodynamic uncertainty relation
• Introduction to dynamical large deviations of Markov processes
• Generic Properties of Stochastic Entropy Production
• Thermodynamic uncertainty relation for time-dependent driving
• Inferring dissipation from current fluctuations
• Inferring entropy production from short experiments
• Dissipation and lag in irreversible processes
• Multidimensional thermodynamic uncertainty relations
• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• Estimating entropy production by machine learning of short-time fluctuating currents
• Steady state statistics of driven diffusions
• Stochastic thermodynamics for active matter
• Unifying Thermodynamic Uncertainty Relations
• Entropy production estimation with optimal current
• Stochastic thermodynamics: From principles to the cost of precision
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Thermodynamic Uncertainty Relation for Arbitrary Initial States
• Bounds on current fluctuations in periodically driven systems
• Faster uphill relaxation in thermodynamically equidistant temperature quenches
• A generalization of the thermodynamic uncertainty relation to periodically driven systems
• Frenetic bounds on the entropy production
• Improving thermodynamic bounds using correlations
• Emergent memory and kinetic hysteresis in strongly driven networks
• Classical pendulum clocks break the thermodynamic uncertainty relation
• A Decomposition of Irreversible Diffusion Processes Without Detailed Balance
• Information-theoretical bound of the irreversibility in thermal relaxation processes
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Optimal thermodynamic uncertainty relation in Markov jump processes
• A unifying picture of generalized thermodynamic uncertainty relations
• Monotone return to steady nonequilibrium
• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States
• Scattering fingerprints of two-state dynamics
• Thermodynamic uncertainty relation for Langevin dynamics by scaling time
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• On correlations and fluctuations of time-averaged densities and currents with general time-dependence

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