Contrasting Work Fluctuations and Distributions in Systems with Short-Range and Long-Range Correlations

Abstract

It is shown that the work fluctuations and work distribution functions are fundamentally different in systems with short-range versus long-range correlations. The two cases considered with long-range correlations are magnetic work fluctuations in an equilibrium isotropic ferromagnet and work fluctuations in a nonequilibrium fluid with a temperature gradient. The long-range correlations in the former case are due to equilibrium Goldstone modes, while in the latter they are due to generic nonequilibrium effects. The magnetic case is of particular interest, since an external magnetic field can be used to tune the system from one with long-range correlations to one with only short-range correlations. It is shown that in systems with long-range correlations the work distribution is extraordinarily broad compared to systems with only short-range correlations. Surprisingly, these results imply that fluctuation theorems such as the Jarzynski fluctuation theorem are more useful in systems with long-range correlations than in systems with short-range correlations.