Extension of the Fluctuation Theorem

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.

Figure 1

Numerically obtained $f_{\tau }(p)$ (bold dashed line) for $v^{*}=1.5$ and $\tau =1.3$, and the ($v^{*}$ independent) extension of the SSFT for $\tau \to \infty$ (bold solid line). Also plotted are the conventional SSFT (thin solid line), and the numerically obtained distribution function $P_{\tau }(pw\tau )$, scaled by its value at zero (thin dashed line).