Temperature and Degrees of Freedom of Potential Energy vs Its Kinetic Counterparts and Their Roles in Decoding Phase Transition

Abstract Temperature, a fundamental metric in thermal energy characterization, encounters intriguing exceptions during phase transitions, where it maintains a constant value despite significant internal energy alterations. Equipartition theorem also failed in interpreting these phenomena. In this study, we introduce a novel framework termed "potential energy temperature (Tpot)" and associated degrees of freedom (Dpot) to provide deeper insights into phase transitions. Our investigations reveal that Tpot diverges considerably from conventional temperature (Tkin) defined by kinetic energy, and Dpot is influenced not only by dimensions in Cartesian coordinate but also by the number of interacting atoms. A noteworthy finding is the correlation between phase changes and increased Dpot, which explains the observed increase in potential energy using the equipartition theorem. Additionally, we identify a sudden change in Tpot during the phase transition, diverging from conventional descriptions. Furthermore, our study unveils unconventional concepts, such as the potential energy of an atom being significantly lower at higher temperatures than at absolute zero. These findings offer a fresh perspective on the phase changes of matter, challenging existing paradigms and providing insights into this complex yet fundamental natural process.