García-García Reinaldo, Domínguez Daniel
Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Río Negro, Argentina.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 May;89(5):052121. doi: 10.1103/PhysRevE.89.052121. Epub 2014 May 14.
We introduce the violation fraction υ as the cumulative fraction of time that a mesoscopic system spends consuming entropy at a single trajectory in phase space. We show that the fluctuations of this quantity are described in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function Φ, which can be interpreted as an entropy associated with the fluctuations of the violation fraction. The function Φ, when evaluated for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations that are relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the probability density function of Φ. We study the steady-state limit of this symmetry in the paradigmatic case of a colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss possible applications of our results for the estimation of free-energy differences from single-molecule experiments.
我们引入违反分数υ，它表示介观系统在相空间单个轨迹上消耗熵所花费时间的累积分数。我们表明，这个量的涨落可以用一种类似于涨落定理的对称关系来描述，该关系涉及一个函数Φ，它可以被解释为与违反分数涨落相关的熵。当针对违反分数的任意随机实现进行评估时，函数Φ在与相关随机熵产生相关的对称变换下是奇函数。这一事实导致了关于Φ概率密度函数的详细涨落定理。我们在光镊拖动胶体粒子通过水溶液的典型案例中研究了这种对称性的稳态极限。最后，我们简要讨论了我们的结果在从单分子实验估计自由能差方面的可能应用。
