2003/11/26 by R. van Zon, E. G. D. Cohen
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.056121
published as Phys. Rev. E 69, 056121 (2004) · 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected and a footnote was added on the d-dimensional case
arxiv created 2003/11/26 · arxiv updated 2009/12/01
Heat fluctuations over a time τin a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all τ. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small τ, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite τ, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.