标题： 相对论涨落定理：理论和显式例子 显示英文标题

标题： Relativistic Fluctuation Theorems: Theory and explicit examples

摘要： 为了揭示非平衡物理和相对论理论如何交织在一起，本文研究了宇宙膨胀下的相对论性布朗运动。 在这一极端非平衡情况下局部产生的熵 ds 的两个涨落定理被提出并证明。 第一个定理，<exp(-ds)>=1，是热力学第二定律的推广，在相对论粒子能量和高宇宙膨胀速率下仍然有效。 由此关系可知，即使宇宙发生坍缩，观察到局部熵减少的概率也是指数级小的。 对于爱因斯坦-德西特宇宙的特殊情况，还推导出另一个关系式 <exp(-ds-dh)>=1，该关系式与第一个关系式同时成立，其中 dh 与哈勃常数成正比。 此外，涨落定理被证明可以提供一个物理标准来解决特殊相对论性布朗运动中出现的已知离散化困境。 提供了具体的例子以及计算非高斯熵涨落的一般方法。 显示英文摘要

摘要： To reveal how nonequilibrium physics and relativity theory intertwine, this articles studies relativistic Brownian motion under cosmic expansion. Two fluctuation theorems for the entropy ds, which is locally produced in this extreme nonequilibrium situation, are presented and proven. The first, <exp(-ds)>=1, is a generalization of the second law of thermodynamics, that remains valid at relativistic particle energies and under high cosmic expansion rates. From this relation follows, that the probability to observe a local reduction of entropy is exponentially small even if the universe was to recollapse. For the special case of the Einstein-de Sitter universe an additional relation, <exp(-ds-dh)>=1, is derived which holds simultaneously with the first relation and where dh is proportional to the Hubble constant. Furthermore, the fluctuation theorems are shown to provide a physical criterion to resolve the known discretization dilemma arising in special-relativistic Brownian motion. Explicit examples and a general method for the computation of non-Gaussian entropy fluctuations are provided.