The analysis of fluctuations generated by a thermal reservoir has produced many results throughout the history of science, ranging from the verification of the atomic hypothesis, running through critical phenomena to the most recent advances in the description of non-equilibrium thermodynamic processes. Motivated by recent theoretical and experimental works, we analyze the non-equilibrium and equilibrium fluctuations caused by a finite and chaotic heat bath in a simple system of interest. The finite bath and system of interest give rise to a non-ergodic composite system when interacting with each other. We have characterized the equilibrium distribution induced by the finite bath and numerically verified the finite-bath fluctuation theorem. We have also verified the convergence of our results to Crooks’ fluctuation theorem as the number of degrees of freedom of the finite bath increases while the non-ergodic character remains.

中文翻译：

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非遍历系统有限浴波动定理的证明

在整个科学史上，对储热器产生的波动的分析已经产生了许多结果，从原子假设的验证，贯穿关键现象到非平衡热力学过程描述的最新进展。根据最新的理论和实验工作，我们在一个简单的感兴趣的系统中分析了由有限的混沌热浴引起的非平衡和平衡波动。当彼此相互作用时，有限浴和感兴趣的系统会产生非遍历的复合系统。我们已经刻画了有限浴引起的平衡分布，并数值验证了有限浴波动定理。