Baiesi Marco, Falasco Gianmaria
Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy.
INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042162. doi: 10.1103/PhysRevE.92.042162. Epub 2015 Oct 29.
While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time-integrated) difference between entrance rate and escape rate in mesoscopic jump systems. Such inflow rate, which is even under time reversal, represents the discrete-state equivalent of the phase-space contraction rate. Indeed, it becomes minus the divergence of forces in the continuum limit to overdamped diffusion. This establishes a formal connection between reversible deterministic systems and irreversible stochastic ones, confirming that fluctuation theorems are largely independent of the details of the underling dynamics.
虽然熵变通常是涨落定理的研究对象，但我们寻求涉及时间对称量的涨落关系，即如果轨迹在时间上反向观测时符号不变的可观测量。我们在介观跳跃系统中发现了关于进入率和逃逸率（时间积分）之差的详细涨落关系和积分涨落关系。这种在时间反演下为偶数的流入率，代表了相空间收缩率的离散态等效量。实际上，在过阻尼扩散的连续极限中，它变为力的散度的负值。这在可逆确定性系统和不可逆随机系统之间建立了一种形式上的联系，证实了涨落定理在很大程度上与基础动力学的细节无关。
