Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems
arXiv:cond-mat/0605548 · doi:10.1007/s10955-006-9252-2
Abstract
A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integrals for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.
arXiv comment20 pages, 2 figures
References in corpus (26)
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Fluctuation theorem for stochastic dynamics
- Path ensembles averages in systems driven far-from-equilibrium
- Macroscopic fluctuation theory for stationary non equilibrium states
- Fluctuations in Stationary non Equilibrium States
- An Extension of the Fluctuation Theorem
- Nonequilibrium fluctuations in a resistor
- Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
- Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
- Path-integral analysis of fluctuation theorems for general Langevin processes
- Non equilibrium current fluctuations in stochastic lattice gases
- Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
- Power and heat fluctuation theorems for electric circuits
- A fluidized granular medium as an instance of the Fluctuation Theorem
- Note on Two Theorems in Nonequilibrium Statistical Mechanics
- Chaotic Hypothesis, Fluctuation Theorem and singularities
- Experimental test of the Gallavotti-Cohen fluctuation theorem in turbulent flows
- SRB states and nonequilibrium statistical mechanics close to equilibrium
- Reexamination of experimental tests of the fluctuation theorem
- Fluctuation relations for a driven Brownian particle
- Fluctuation symmetries for work and heat
- Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas
- Steady shear flow thermodynamics based on a canonical distribution approach
- Out of equilibrium dynamics of the toy model with mode coupling and trivial Hamiltonian
Cited by in corpus (51)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The large deviation approach to statistical mechanics
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
- Dynamics of a Brownian circle swimmer
- Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
- On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
- Stochastic thermodynamics for delayed Langevin systems
- Non-equilibrium fluctuations for linear diffusion dynamics
- Probability density functions of work and heat near the stochastic resonance of a colloidal particle
- Work fluctuations in a time-dependent harmonic potential: rigorous results and beyond the overdamped limit
- Asymptotics of work distributions in non-equilibrium systems
- Stick-slip motion of solids with dry friction subject to random vibrations and an external field
- Thermodynamic time asymmetry in nonequilibrium fluctuations
- Invariant quantities in shear flow
- Reinforcement learning of rare diffusive dynamics
- Inertial Effects in Nonequilibrium Work Fluctuations by a Path Integral Approach
- Anomalous fluctuation relations
- Nonequilibrium Steady State Driven by a Nonlinear Drift Force
- Path integral approach to random motion with nonlinear friction
- Thermodynamic Bounds on Symmetry Breaking in Linear and Catalytic Biochemical Systems
- Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations
- Feynman-Kac equation for anomalous processes with space- and time-dependent forces
- A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems
- Properties of Nonequilibrium Steady States: a Path Integral Approach
- Nonequilibrium steady state thermodynamics and fluctuations for stochastic systems
- The Heat Distribution in a Logarithm Potential
- Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models
- Quantifying the validity and breakdown of the overdamped approximation in stochastic thermodynamics: Theory and experiment
- Work and heat distributions for a Brownian particle subjected to an oscillatory drive
- Exact Nonequilibrium Work Generating Function for a Small Classical System
- Heat fluctuations for underdamped Langevin dynamics
- A path integral formalism for non-equilibrium Hamiltonian statistical systems
- Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle
- Time and Thermodynamics Extended Discussion on "Time & clocks: A thermodynamic approach"
- Irreversible Circulation of Fluctuation and Entropy Production
- Transient photocurrent and optical absorption of disordered thin-film semiconductors: in-depth injection and nonlinear response
- Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations
- Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
- Fluctuation theorem for the renormalized entropy change in the strongly nonlinear nonequilibrium regime
- Dynamical fluctuations for periodically driven diffusions
- Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations
- Macroscopic proof of the Jarzynski-Wojcik fluctuation theorem for heat exchange
- Work distribution function for a Brownian particle driven by a nonconservative force
- Influence of rotational force fields on the determination of the work done on a driven Brownian particle
- Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold
- Fluctuation relation in continuous-time random walks driven by an external field
- Pattern Formation in Thermal Convective Systems: Spatio-temporal Thermal Statistics, Emergent Flux, and Local Equilibrium
- Irreversibility of stochastic state transitions in Langevin systems with odd elasticity
- The Steady State Distribution of the Master Equation
- Role of parity transformation for the fluctuation theorem: Limit cycle and symmetry breaking