Challenges in thermodynamics: Irreversible processes, nonextensive entropies, and systems without equilibrium states*

Recent works on evaporation and condensation demonstrate that even these simplest irreversible processes, studied for over 100 years, are not well understood. In the case of a liquid evaporating into its vapor, the liquid temperature is constant during evaporation and the evaporation flux is governed by the heat transfer from the hotter vapor into the colder liquid. Whether liquid evaporates into its own vapor or into the vacuum, the irreversible pathway in the process goes through a number of steps which quickly lead to the steady-state conditions with mechanical equilibrium in most parts of the system—the fact overlooked in all previous studies. Even less is known about general rules which govern systems far from equilibrium. Recently, it has been demonstrated that a work done in an irreversible process can be related to the free energy difference between equilibrium states joined by the process. Finally, a real challenge in thermodynamics is a description of living systems since they do not have equilibrium states, are nonextensive, (i.e., they cannot be divided into subsystems), and cannot be isolated. Thus, their proper description requires new paradigms in thermo dynamics.