QUANTUM THERMODYNAMICS AT THE CRITICAL POINTS DURING MELTING AND SOLIDIFICATION PROCESSES

Abstract. Phase transitions are ubiquitous, exist in all fields of science in one form or another. The most common example in condensed matter physics is the Landau thermal phase transition, which is from a liquid to a solid phase or vice versa. Here, we systematically explore and develop unequivocal the-oretical strategies, going beyond the total-energy minimization techniques to understand what constitutes the thermal phase transition. We prove the ex-istence of finite-temperature continuous quantum phase transitions (CTQPT) during solidification and melting processes such that CTQPT is responsible for all first-order thermal phase transitions. In fact, this CTQPT is related to chem-ical reactions where the quantum fluctuations are caused by thermal energies, and it may occur maximally for temperatures much higher than zero-Kelvin. To extract the quantitative information related to CTQPT, we use the ion-ization energy theory to derive the electronic-excitation and atomic-disorder (or symmetry-breaking) entropies. Subsequently, we exploit the energy level spacing renormalization group method to renormalize (i) the Bose-Einstein distribution and (ii) the specific heat capacity. We also conclude that the proofs developed herein can lead us to the unification of thermodynamics and quantum mechanics such that one can evaluate the changes in specific heat due to wave function transformations (quantum mechanical effects) when one crosses over from a solid to a liquid or vice versa at a constant temperature