Entropy fluctuation theorems in driven open systems: application to electron counting statistics

TL;DR

This paper derives universal fluctuation theorems for entropy production in driven open systems, linking theoretical results with electron counting experiments on quantum dots to validate the theorems and explore entropy fluctuations.

Contribution

It introduces three new integral fluctuation theorems for different entropy production mechanisms in driven systems, unifying and extending previous results.

Findings

Universal inequality for entropy production in nonequilibrium transformations

Fluctuation theorems applicable to electron counting in quantum dots

Simulations confirm entropy distribution behavior under various driving protocols

Abstract

The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: an arbitrary nonequilibrium transformation always produces a change in the total entropy production greater or equal than the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.