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The analysis of fluctuations generated by a thermal reservoir has produced many results throughout the history of physics, 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 equilibrium and non-equilibrium fluctuations caused by a finite bath of deterministic and chaotic dynamics when weakly coupled with a system of interest whose total system is approximately ergodic. In particular, in this work, we tested the heat theorem and the fluctuation theorem for finite baths considering the mentioned model.  In both cases, we verified the agreement between numerical results and analytic estimates.