Analytical results and universal behavior in fast thermal equilibration protocols

When a system deviates from equilibrium, it is possible to manipulate and control it to drive it towards equilibrium within finite time t_{f}, even by reducing its natural relaxation timescale τ_{relax}. Although numerous theoretical and experimental studies have explored these shortcut protocols, few have yielded analytical results for the probability distribution of the work, heat, and produced entropy. In this study, we propose a two-step protocol that captures the essential characteristics of more general protocols and provides an analytical solution for the relevant thermodynamic probability distributions. Additionally, we present evidence that for a very short protocol duration t_{f}≪τ_{relax}, all protocols exhibit universal behavior for the ratio of probability distribution functions of positive and negative work, heat, and the produced entropy.