Superstatistical generalization of the work fluctuation theorem

TL;DR

This paper extends the work fluctuation theorem to systems with spatial and temporal temperature fluctuations, revealing slower decay of work fluctuations which impacts micro and nano device design.

Contribution

It introduces a superstatistical approach to generalize the fluctuation theorem for nonuniform temperature distributions, especially with chi-square statistics.

Findings

Generalized fluctuation theorem based on q-exponentials

Slower decay of work fluctuations compared to classical theorem

Implications for micro and nano structure design

Abstract

We derive a generalized version of the work fluctuation theorem for nonequilibrium systems with spatio-temporal temperature fluctuations. For chi-square distributed inverse temperature we obtain a generalized fluctuation theorem based on q-exponentials, whereas for other temperature distributions more complicated formulae arise. Since q-exponentials have a power law decay, the decay rate in this generalized fluctuation theorem is much slower than the conventional exponential decay. This implies that work fluctuations can be of relevance for the design of micro and nano structures, since the work done on the system is relatively much larger than in the conventional fluctuation theorem.