Refined Second Law of Thermodynamics for fast random processes

Abstract

We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport. General discussion is illustrated by numerical analysis of a model for micron-size particle manipulated by optical tweezers.

17 pages

References in corpus (12)

• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Dissipation: The phase-space perspective
• Optimal finite-time processes in stochastic thermodynamics
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Fluctuation Relations for Diffusion Processes
• Steady state statistics of driven diffusions
• Boundary layers in stochastic thermodynamics
• Dynamical randomness, information, and Landauer's principle
• On Thermostats: Isokinetic or Hamiltonian? finite or infinite?
• Fluctuation Theorem and Chaos
• Landauer's erasure principle in non-equilibrium systems

Cited by in corpus (115)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• High-precision test of Landauer's principle in a feedback trap
• Universal trade-off relation between power and efficiency for heat engines
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Speed Limit for Classical Stochastic Processes
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Engineered swift equilibration of a Brownian particle
• Finite-time Landauer principle
• The geometry of thermodynamic control
• Thermodynamic and Logical Reversibilities Revisited
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Optimal finite-time erasure of a classical bit
• Controlling the speed and trajectory of evolution with counterdiabatic driving
• Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
• Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
• Information and thermodynamics: fast and precise approach to Landauer's bound in an underdamped micro-mechanical oscillator
• Finite-time erasing of information stored in fermionic bits
• Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
• Universal Bound on Energy Cost of Bit Reset in Finite Time
• Optimal finite-time bit erasure under full control
• Optimal Control of Overdamped Systems
• Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks
• Information and thermodynamics: Experimental verification of Landauer's erasure principle
• Optimal protocols for slowly-driven quantum processes
• Detailed Jarzynski Equality applied on a Logically Irreversible Procedure
• Minimal dissipation in processes far from equilibrium
• Speed limit for a highly irreversible process and tight finite-time Landauer's bound
• Efficiency versus Speed in Quantum Heat Engines: Rigorous Constraint from Lieb-Robinson Bound
• Housekeeping and excess entropy production for general nonlinear dynamics
• Thermal bath Engineering for Swift Equilibration
• Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
• Nanoscale virtual potentials using optical tweezers
• Dynamics of information erasure and extension of Landauer's bound to fast processes
• Dependence of dissipation on the initial distribution over states
• Thermodynamic transformations of nonequilibrium states
• Maximum work extraction and implementation costs for non-equilibrium Maxwell's demons
• Finite-time adiabatic processes: derivation and speed limit
• Geometric decomposition of entropy production into excess, housekeeping and coupling parts
• A unified, geometric framework for nonequilibrium protocol optimization
• Deep learning probability flows and entropy production rates in active matter
• A fast semi-discrete optimal transport algorithm for a unique reconstruction of the early Universe
• On how nanomechanical systems can minimize dissipation
• Fundamental energy cost of finite-time computing
• "Information-Friction" and its implications on minimum energy required for communication
• Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems
• E. Schrödinger's 1931 paper "On the Reversal of the Laws of Nature" ["Über die Umkehrung der Naturgesetze",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]
• Thermodynamic interpretation of Wasserstein distance
• Finite-time Landauer principle beyond weak coupling
• Fundamental relation between entropy production and heat current
• Fundamental bounds on precision and response for quantum trajectory observables
• Optimality of non-conservative driving for finite-time processes with discrete states
• On work and heat in time-dependent strong coupling
• Heat release by controlled continuous-time Markov jump processes
• Thermodynamic speed limits for mechanical work
• Work needed to drive a thermodynamic system between two distributions
• Optimal protocols and universal time-energy bound in Brownian thermodynamics
• Taming the time evolution in overdamped systems: shortcuts elaborated from fast-forward and time-reversed protocols
• Information flow and optimal protocol for Maxwell's demon single electron pump
• Landauer Principle and Thermodynamics of Computation
• Stochastic Optimal Control as Non-equilibrium Statistical Mechanics: Calculus of Variations over Density and Current
• On extremals of the entropy production by "Langevin-Kramers" dynamics
• Energetic cost of feedback control
• An application of Pontryagin's principle to Brownian particle engineered equilibration
• On the efficiency of heat engines at the micro-scale and below
• Adiabatic computing for optimal thermodynamic efficiency of information processing
• Time reversals of irreversible quantum maps
• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• The Differential Entropy of Mixtures: New Bounds and Applications
• Optimization of stochastic thermodynamic machines
• Refining Landauer's Stack: Balancing Error and Dissipation When Erasing Information
• On the use of stochastic differential geometry for non-equilibrium thermodynamics modeling and control
• Speed limit for open systems coupled to general environments
• Thermodynamic bounds on generalized transport: From single-molecule to bulk observables
• Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport
• Pros and cons of swimming in a noisy environment
• Optimal Control of Underdamped Systems: An Analytic Approach
• Conditional entropy and Landauer principle
• Hybrid master equation for calorimetric measurements
• Feedback traps for virtual potentials
• Quantitative analysis of Clausius inequality
• Stochastic thermodynamics of nonharmonic oscillators in high vacuum
• Inferring entropy production from time-dependent moments
• Reliability and operation cost of underdamped memories during cyclic erasures
• Thermodynamics of majority-logic decoding in information erasure
• Minimal work protocols for inertial particles in non-harmonic traps
• Reset and switch protocols at Landauer limit in a graphene buckled ribbon
• Infinite variety of thermodynamic speed limits with general activities
• Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics
• Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation
• Entropy production given constraints on the energy functions
• Efficiently driving F${}_1$ molecular motor in experiment by suppressing nonequilibrium variation
• Optimal control of levitated nanoparticles through finite-stiffness confinement
• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Erasing a majority-logic bit
• Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transport
• Experimentally achieving minimal dissipation via thermodynamically optimal transport
• Role of interactions in non-equilibrium transformations
• Work statistics at first-passage times
• Classical uncertainty relations and entropy production in non-equilibrium statistical mechanics
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
• Wasserstein distance in speed limit inequalities for Markov jump processes
• A Shortcut to Finite-time Memory Erasure
• Evading Thermodynamic Uncertainty Relations via Asymmetric Dynamic Protocols
• On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula
• Decomposition of metric tensor in thermodynamic geometry in terms of relaxation timescales
• Accelerating the heat diffusion: fast thermal relaxation of a microcantilever
• A perspective on Lindblad's Non-Equilibrium Entropy
• Global thermodynamic manifold for conservative control of stochastic systems
• Virtual double-well potential for an underdamped oscillator created by a feedback loop
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference
• Improving the efficiency of finite-time memory erasure with potential barrier shaping
• Time-cost-error trade-off relation in thermodynamics: The third law and beyond