  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. 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.
