2025/04/08 by Pierre Nazé, Nazé, Pierre
Physics and Astronomy · #stochastic dynamics and bifurcation #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2504.05836
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped regime for any switching time. The white noise Brownian motion in a harmonic linear stiffening trap illustrates the result. The work probability distribution is non-tabulated, with positive, semi-finite support, diverging at the minimal value, and non-Gaussian. An analysis of the range of validity of linear response is made by using the self-consistent criterion of the fluctuation-dissipation relation. The first, second, third, and fourth moments are correctly calculated for small perturbations.