Entropic bounds on currents in Langevin systems

Abstract

We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency---Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet---can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the Second Law. Finally, we discuss the connection between heat and entropy in a non-thermal situation where the friction and noise intensity are state-dependent.

18 pages, 2 figures

References in corpus (9)

• Thermodynamic uncertainty relation for biomolecular processes
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Relativistic Brownian Motion
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• An all-optical nanomechanical heat engine
• Brownian motion with dry friction: Fokker-Planck approach
• Stick-slip motion of solids with dry friction subject to random vibrations and an external field
• Singular features in noise-induced transport with dry friction

Cited by in corpus (63)

• Thermodynamic uncertainty relation for time-dependent driving
• Cycling tames power fluctuations near optimum efficiency
• Multidimensional thermodynamic uncertainty relations
• Estimating entropy production by machine learning of short-time fluctuating currents
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• The dissipation-time uncertainty relation
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Theoretical Perspectives on Biological Machines
• Improving thermodynamic bounds using correlations
• Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry
• Speed Limits for Macroscopic Transitions
• Classical pendulum clocks break the thermodynamic uncertainty relation
• Entropy production in systems with unidirectional transitions
• Bounds in Nonequilibrium Quantum Dynamics
• Optimal thermodynamic uncertainty relation in Markov jump processes
• Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force
• Brownian heat engine with active reservoirs
• A unifying picture of generalized thermodynamic uncertainty relations
• Geometric decomposition of entropy production into excess, housekeeping and coupling parts
• Universal form of thermodynamic uncertainty relation for Langevin dynamics
• Thermodynamic Bounds on Coherent Transport in Periodically Driven Conductors
• Local detailed balance across scales: from diffusions to jump processes and beyond
• Thermodynamic cost, speed, fluctuations, and error reduction of biological copy machines
• Thermodynamic interpretation of Wasserstein distance
• Thermodynamic uncertainty relation to assess biological processes
• Field-Theoretic Thermodynamic Uncertainty Relation -- General formulation exemplified with the Kardar-Parisi-Zhang equation
• Fluctuations of entropy production of a run-and-tumble particle
• Entropy production in Master Equations and Fokker-Planck Equations: facing the coarse-graining and recovering the information loss
• Thermodynamic Uncertainty Relation in Interacting Many-Body Systems
• Dissipation, quantum coherence, and asymmetry of finite-time cross-correlations
• Exactly solvable two-terminal heat engine with asymmetric Onsager coefficients: Origin of the power-efficiency bound
• Universal Property of the Housekeeping Entropy Production
• Flow of Energy and Information in Molecular Machines
• Thermodynamic uncertainty for run-and-tumble type processes
• Effective Entropy Production and Thermodynamic Uncertainty Relation of Active Brownian Particles
• Perspective: Time irreversibility in systems observed at coarse resolution
• Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines
• Thermodynamic bounds on generalized transport: From single-molecule to bulk observables
• Precision bound and optimal control in periodically modulated continuous quantum thermal machines
• Achieving Carnot efficiency in a finite-power Brownian Carnot cycle with arbitrary temperature difference
• An ordered set of power-efficiency trade-offs
• Optimal Control of Underdamped Systems: An Analytic Approach
• Carnot efficiency and zero-entropy-production rate do not guarantee reversibility of a process
• Compatibility of Carnot efficiency with finite power in an underdamped Brownian Carnot cycle in small temperature-difference regime
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• R. Fürth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", \textit{Zeitschrift für Physik,} \textbf{81} 143-162]
• Designing circle Swimmers: Principles and strategies
• The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system
• Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities
• Jensen bound for the entropy production rate in stochastic thermodynamics
• Maximum Power of Coupled-Qubit Otto Engines
• Improved estimation for energy dissipation in biochemical oscillations
• Speed limits to fluctuation dynamics
• Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport
• Power-efficiency trade-off for finite-time quantum harmonic Otto heat engine via phase-space approach
• A case study of thermodynamic bounds for chemical kinetics
• Experimentally accessible measurement of irreversibility in stochastic systems by categorizing single-molecule displacements
• The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation
• Inertia Tames Fluctuations in Autonomous Stationary Heat Engines
• Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations
• Thermodynamic uncertainty relation for systems with active Ornstein-Uhlenbeck particles
• Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales