Abstract

Cross phenomena, representing responses of a system to external stimuli, are ubiquitous from quantum to macro scales. Through flux equations based on the combined law of thermodynamics, theory of cross phenomena is developed and applied to thermoelectricity, thermodiffusion, diffusion, electromigration, electrocaloric and electromechanical effects, and thermal expansion. It is shown that the coefficient matrix connecting the driving forces and the fluxes is intrinsically diagonal, and thus symmetrical in accordance with Onsager’s reciprocal relations (https://doi.org/10.1080/21663831.2022.2054668). In order to predict the emergent cross phenomena, the zentropy theory is developed to represent the total entropy of a system (macrostate) by a nested formula with two portions: the weighted average of the entropies of statistically significant configurations of the system (microstates) and the statistical distribution of the microstates in the system. It is shown that when the microstates are represented by mixed quantum states, the free energy of each microstate should be used in their partition functions instead of internal energy commonly used in the literature (https://doi.org/10.1007/s11669-022-00942-z).