Symmetry for the duration of entropy-consuming intervals

Abstract

We introduce the violation fraction $\upsilon$ as the cumulative fraction of time that a mesoscopic system spends consuming entropy at a single trajectory in phase space. We show that the fluctuations of this quantity are described in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function, $\Phi$, which can be interpreted as an entropy associated to the fluctuations of the violation fraction. The function $\Phi$, when evaluated for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations which are relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the probability density function of $\Phi$. We study the steady-state limit of this symmetry in the paradigmatic case of a colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss on possible applications of our results for the estimation of free-energy differences from single molecule experiments.

arXiv comment11 pages, 4 figures. Last revised. Version accepted for publication in Phys. Rev. E

References in corpus (26)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• 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
• Path ensembles averages in systems driven far-from-equilibrium
• Steady State Thermodynamics of Langevin Systems
• The Nonequilibrium Thermodynamics of Small Systems
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Three detailed fluctuation theorems
• The Three Faces of the Second Law: I. Master Equation Formulation
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Non-equilibrium work fluctuations for oscillators in non-Markovian baths
• Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
• Large deviations and nontrivial exponents in coarsening systems
• Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process
• Unifying approach for fluctuation theorems from joint probability distributions
• Fluctuation relations for anomalous dynamics
• Joint probability distributions and fluctuation theorems
• Non-adiabatic entropy production for non-Markov dynamics
• Simple one-dimensional quantum-mechanical model for a particle attached to a surface
• Duration of local violations of the second law of thermodynamics along single trajectories in phase space

Cited by in corpus (1)

• Duration of local violations of the second law of thermodynamics along single trajectories in phase space