The origin of irreversibility and thermalization in thermodynamic processes

Abstract

Understanding the origin of irreversibility in thermodynamics has been a fundamental scientific challenge and puzzle for nearly a century. Initially, the discussions related to classical thermodynamic systems, but recently quantum systems became the main focus. Explanations have often been sought by reference to classical equations of motion, which are time-reversible. We conjecture that the origin of irreversibility lies in energy dissipation, a term that is at the core of the Second Law of thermodynamics. However, thermodynamic irreversibility is distinct from time-irreversibility. A system in thermodynamic equilibrium may have reached this state via a deterministic, integrable and therefore time-reversible process, or, alternatively, via an irreversible route, both resulting in thermodynamically indistinguishable states. The process with time-reversible history may become irreversible by a process called thermalization, which occurs when the system loses memory of its history without the necessity of energy dissipation. Quantum systems do this by losing phase coherence; for classical systems the decoherence is at zero frequency, due to loss of time correlation. More generally, not only equilibrium systems may have lost memory of their history. A common cause of memory loss is probabilistic/stochastic events, which are not deterministic and take place only with a certain probability at any given time. In contrast to thermalization, equilibration involves energy dissipation within a system or to the surroundings or by decrease of concentration of the system. Time-reversibility is not related to system size, and the fluctuation theorem is a probabilistic and not a deterministic phenomenon and therefore not suited to provide an understanding of the irreversibility of time in thermodynamic systems. There are also processes which are both dissipative and probabilistic, such as the radiative or non-radiative decay of electronically excited states. Dissipation of a given energy into multiple smaller energy quanta (heat) is by itself not fully reversible for kinetic reasons. It is kinetically a first-order probabilistic process, whereas the reverse is a second- or higher-order process. Thermodynamics provides empirical laws, developed for conventional matter as we know it on planet Earth and in our laboratories. Of relevance here is the Second Law, also called the arrow of time, stating that spontaneous processes take place for isolated systems with increasing entropy. It is assumed to hold also for the universe as a whole. However, over the distances of individual galaxies, self-gravitation leads to conditions where the kinetic energy of the system decreases while the total energy increases, pretending negative heat capacity, and it allows the formation of black holes. This requires an extension of the Second Law. This review aims at presenting an overarching tutorial clarification of the subject.