Fluctuation theorems for harmonic oscillators

Abstract

We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together with non equilibrium steady states. Fluctuations Relations are obtained experimentally for both the work and the heat, for the stationary and transient evolutions. A Stationary State Fluctuation Theorem is verified for the two time prescriptions of the torque. But a Transient Fluctuation Theorem is satisfied for the work given to the system but not for the heat dissipated by the system in the case of linear forcing. Experimental observations on the statistical and dynamical properties of the fluctuation of the angle, we derive analytical expressions for the probability density function of the work and the heat. We obtain for the first time an analytic expression of the probability density function of the heat. Agreement between experiments and our modeling is excellent.

References in corpus (28)

• 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
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Dynamical ensembles in stationary states
• Steady State Thermodynamics of Langevin Systems
• Fluctuation theorems for stochastic dynamics
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• An Extension of the Fluctuation Theorem
• Nonequilibrium fluctuations in a resistor
• Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
• 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
• Work fluctuation theorems for harmonic oscillators
• Injected Power Fluctuations in Langevin Equation
• Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
• A two-state kinetic model for the unfolding of single molecules by mechanical force
• Experimental test of the Gallavotti-Cohen fluctuation theorem in turbulent flows
• On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium
• Reexamination of experimental tests of the fluctuation theorem
• Power fluctuations in stochastic models of dissipative systems
• Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models
• Work distribution and path integrals in general mean-field systems
• The distribution function of entropy flow in stochastic systems
• Experimental study of work fluctuations in a harmonic oscillator

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• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
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• Inertial Effects in Nonequilibrium Work Fluctuations by a Path Integral Approach
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• Classical open systems with nonlinear nonlocal dissipation and state-dependent diffusion: Dynamical responses and the Jarzynski equality
• Heat fluctuations for underdamped Langevin dynamics
• The Heat Distribution of the Underdamped Langevin Equation
• Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable non-dissipative non-ergodic model
• Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains
• Probabilistic work extraction on a classical oscillator beyond the second law
• Extracting work from a single reservoir in the non-Markovian underdamped regime
• Exact distribution for work and stochastic efficiency of an isothermal machine
• Work fluctuations in a nematic liquid crystal
• Probabilities for informational free lunches in stochastic thermodynamics
• Current loops and fluctuations in the zero-range process on a diamond lattice
• Exponential peak and scaling of work fluctuations in modulated systems
• Energetics of the single-well undamped stochastic oscillators
• Work distribution function for a Brownian particle driven by a nonconservative force
• Fluctuation theorems in inhomogenious media under coarse graining
• Effects of the kinetic energy in heat for overdamped systems
• Heat Distribution of Relativistic Brownian Motion
• Heat fluctuations in the logarithm-harmonic potential
• Statistical properties of the energy flux between two NESS thermostats
• Energy fluctuations in a biharmonically driven nonlinear system