Extension of Classical Thermodynamics to Nonequilibrium Polarization

Thermodynamics concerns two kinds of states, the equilibrium ones (classical thermodynamics) and the nonequilibrium ones (nonequilibrium thermodynamics). The classical thermodynamics is an extremely important theory for macroscopic properties of systems in equilibrium, but it can not be fully isolated from nonequilibrium states and irreversible processes. Therefore, within the framework of classical thermodynamics, it is significant to explore a new method to solve the questions in the nonequilibrium state. Furthermore, this treatment should be helpful for getting deep comprehension and new applications of classical thermodynamics. For an irreversible process, thermodynamics often takes the assumption of local equilibrium, which divides the whole system into a number of macroscopic subsystems. If all the subsystems stand at equilibrium or quasi-equilibrium states, the thermodynamic functions for a nonequilibrium system can be obtained by some reasonable treatments. However, the concept of local equilibrium lacks the theoretical basis and the expressions of thermodynamic functions are excessively complicated, so it is hard to be used in practice. Leontovich[1] once introduced a constrained equilibrium approach to treat nonequilibrium states within the framework of classical thermodynamics, which essentially maps a nonequilibrium state to a constrained equilibrium one by imposing an external field. In other words, the definition of thermodynamic functions in classical thermodynamics is firstly used in constrained equilibrium state, and the following step is how to extend this definition to the corresponding nonequilibrium state. This theoretical treatment is feasible in principle, but has not been paid much attention to yet. This situation is possibly resulted from the oversimplified descriptions of the Leontovich’s approach in literature and the lack of practical demands. Hence on the basis of detailed analysis of additional external parameters, we derive a more general thermodynamic formula, and apply it to the case of nonequilibrium polarization. The results show that the nonequilibrium solvation energy in the continuous medium can be obtained by imposing an appropriate external electric field, which drives the nonequilibrium state to a constrained equilibrium one meanwhile keeps the charge distribution and polarization of medium fixed.