Fluctuation Relations for Stochastic Systems far from Equilibrium

Fluctuations are of great importance in systems of small length and energy scales. Measuring the pulling of single molecules or the stationary fiow of mesospheres dragged through a viscous media enables the direct analysis of work and entropy distributions. These probability distributions are the result of a large number of repetitions of the same experiment. Due to the small scale of these experiments, the outcome can vary significantly from one realization to the next. Strong theoretical predictions exist, collectively called Fluctuation Theorems, that restrict the shape of these distributions due to an underlying time reversal symmetry of the microscopic dynamics. Fluctuation Theorems are the strongest existing statements on the entropy production of systems that are out of equilibrium.

Being the most important ingredient for the Fluctuation Theorems, the probability distribution of the entropy change is itself of great interest. Using numerically exact methods we characterize entropy distributions for various stochastic reaction-diffusion systems that present different properties in their underlying dynamics. We investigate these systems in their steady states and in cases where time dependent forces act on them. This study allows us to clarify the connection between the microscopic rules and the resulting entropy production. The present work also adds to the discussion of the steady state properties of stationary probabilities and discusses a non-equilibrium current amplitude that allows us to quantify the distance from equilibrium. The presented results are part of a greater endeavor to find common rules that will eventually lead to a general understanding of non-equilibrium systems.