2023/10/09 by Nazé, Pierre
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2310.05747
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent probability density function of the thermodynamic work evolving in the switching time is solved as a special case. From such a relation, I prove Jarzynski's equality and Crook's fluctuation theorem. The particular case of a Gaussian distribution for slowly-varying processes is derived as well at the end.