Closed Surface Thermodynamics: A Geometric Theory of Heat, Entropy, and Phase Transitions

This work introduces a new theoretical framework for thermodynamics based on the vibrational behavior of closed surfaces. Departing from traditional particle-based models, we define temperature as a function of modal frequency, entropy as a measure of surface pattern diversity, and heat capacity as the rate at which new vibrational modes can be supported. In this Closed Surface Thermodynamic Framework, phase transitions are interpreted as modal collapses or reconfigurations, and thermal conduction emerges as the propagation of vibrational resonance across curved surface gradients. Radiation is understood as the rupture of high-frequency modal patterns, leading to the emission of massless ripple modes (photons). We apply the theory to various real-world systems—including crystals, polymers, water, membranes, and radiative emitters—and demonstrate how material-specific behaviors such as specific heat, thermal conductivity, and emission thresholds can be geometrically predicted. The framework opens new possibilities for energy harvesting, sensor technology, and materials engineering by treating matter as modifiable vibrational architecture. This geometric perspective unifies heat, entropy, phase change, and radiation under a single physical principle: the structured oscillation of closed surfaces. Author Tetsuo Konno (今野哲夫)https://orcid.org/0009-0002-1842-7865