Non-equilibrium work fluctuations for oscillators in non-Markovian baths

Abstract

We study work fluctuation theorems for oscillators in non-Markovian heat baths. By calculating the work distribution function for a harmonic oscillator with motion described by the generalized Langevin equation, the Jarzynski equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT) are shown to be exact. In addition to this derivation, numerical simulations of anharmonic oscillators indicate that the validity of these nonequilibrium theorems do not depend on the memory of the bath. We find that the JE and the CT are valid under many oscillator potentials and driving forces whereas the TFT fails when the driving force is asymmetric in time and the potential is asymmetric in position.

7 pages, 3 figures

References in corpus (15)

• A nonequilibrium equality for free energy differences
• 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
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• The Nonequilibrium Thermodynamics of Small Systems
• The Fluctuation Theorem as a Gibbs Property
• Nonequilibrium fluctuations in a resistor
• A fluidized granular medium as an instance of the Fluctuation Theorem
• Work fluctuation theorems for harmonic oscillators
• Reexamination of experimental tests of the fluctuation theorem
• Fluctuation symmetries for work and heat
• Work distribution functions in polymer stretching experiments

Cited by in corpus (45)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Fluctuation theorems for stochastic dynamics
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• Irreversible effects of memory
• Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
• Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control
• Experimental evidence of non-Gaussian fluctuations near a critical point
• Work and dissipation fluctuations near the stochastic resonance of a colloidal particle
• Entropy production and work fluctuation relations for a single particle in active bath
• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
• Current fluctuations in stochastic systems with long-range memory
• Work fluctuations for a Brownian particle in a harmonic trap with fluctuating locations
• Heat flow due to time-delayed feedback
• Fluctuation relations for anomalous dynamics
• Quantum Smoluchowski equation for driven systems
• On the stochastic thermodynamics of fractional Brownian motion
• Modulated two-level system : Exact work statistics
• Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
• Thermodynamic uncertainty relation for time-delayed Langevin systems
• Uncertainty relations for time-delayed Langevin systems
• Normal and Anomalous Fluctuation Relations for Gaussian Stochastic Dynamics
• Explicit solution of the generalised Langevin equation
• Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
• Non-adiabatic entropy production for non-Markov dynamics
• Classical open systems with nonlinear nonlocal dissipation and state-dependent diffusion: Dynamical responses and the Jarzynski equality
• Enhanced directionality of active processes in a viscoelastic bath
• Stochastic thermodynamics of a probe in a fluctuating correlated field
• Open Quantum Dynamics Theory for Non-Equilibrium Work: Hierarchical Equations of Motion Approach
• Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable non-dissipative non-ergodic model
• Microcanonical work and fluctuation relations for an open system: An exactly solvable model
• Heat generation and transport due to time-dependent forces
• Nonequilibrium fluctuation theorems in the presence of a time-reversal symmetry-breaking field and nonconservative forces
• Non-equilibrium fluctuation theorems in the presence of local heating
• Extracting work from a single reservoir in the non-Markovian underdamped regime
• Microreversibility and driven Brownian motion with hydrodynamic long-time correlations
• Asymmetry of the work probability distribution
• The Jarzynski equality in van der Pol and Rayleigh oscillators
• Work probability distribution and tossing a biased coin
• Transient State Work Fluctuation Theorem for a Driven Classical System
• Role of fluctuations in membrane models: thermal versus non-thermal
• Fluctuation relation in continuous-time random walks driven by an external field
• Generalized fluctuation theorems for classical systems
• Symmetry for the duration of entropy-consuming intervals
• Duration of local violations of the second law of thermodynamics along single trajectories in phase space