Abstract
In this work we study the distribution function for the total entropy production of a Brownian particle embedded in a non-Markovian thermal bath. The problem is studied in the overdamped approximation of the generalized Langevin equation, which accounts for a friction memory kernel characteristic of a Gaussian colored noise. The problem is studied in two physical situations: (i) when the particle in the harmonic trap is subjected to an arbitrary time-dependent driving force; and (ii) when the minimum of the harmonic trap is arbitrarily dragged out of equilibrium by an external force. By assuming a natural non Markovian canonical distribution for the initial conditions, the distribution function for the total entropy production becomes a non Gaussian one. Its characterization is then given through the first three cumulants.
Highlights
The study of fluctuation theorems (FTs) continues to be a topic of great interest in statistical mechanics of small systems out of equilibrium
Its validity was proven for two exactly solvable models : (i) the Brownian particle is in a harmonic trap and it is subjected to an external time-dependent force and; (ii) the minimum of the trap potential is arbitrarily dragged out of equilibrium with a time-dependent protocol
We must mention that the theorem for both the ordinary and charged harmonic oscillator was proven only when the initial condition is canonically distributed at equilibrium with the Markovian thermal bath
Summary
The study of fluctuation theorems (FTs) continues to be a topic of great interest in statistical mechanics of small systems out of equilibrium. The main results reported in [4,28,29,30], are the following: the total entropy production (TEP), denoted as ∆stot , along a single stochastic trajectory, which involves both the particle entropy and entropy production in the surrounding medium, satisfies the integral fluctuation theorem (IFT) It is expressed as he−∆stot i = 1, for canonical initial conditions when the particle is arbitrarily driven by time-dependent external forces over a finite time interval (the transient case). Our main contribution in this work is to show that when the harmonic oscillator is embedded in a non Markovian thermal bath, the change in the total entropy production presents a non-Gaussian distribution function This characteristic comes from the preparation of the system in the initial condition, which in our case is assumed to satisfy a natural non Markovian canonical distribution consistently with the non Markovian heat bath [38,39].
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