Symmetries of cyclic work distributions for an isolated harmonic oscillator (Q2867207)

The verification of Crooks and Jarzynski fluctuation-dissipation relationships has become an active field of investigations within nonequilibrium thermodynamics and statistical mechanics. In order to get a deeper insight into how the outcomes of the mechanical processing of a system forward and backwards, while both being started from the same canonical equilibrium at temperature \(T\), can be related (e.g. Crooks and Jarzynski (in)equalities), a careful calculation or examination of a genuine experimental data collection of the work probability distribution is necessary. The present paper shows a pedagogical attitude and aims at calculating work distributions for an isolated harmonic oscillator, by using a geometric and pictorial approach. In doing so, a broader -- than hitherto known -- symmetry of the distribution of work for the forward process is uncovered. Fluctuation effects in the related quantum case are investigated as well.