Quantization of nonequilibrium heat transport models based on isomorphism and gauge symmetry

The diffusive model in a local thermal equilibrium medium has been well established for classical heat transport. In this study, we investigated the gauge potential formulation of a heat transfer model in a non equilibrium system within classical and quantum frameworks. To achieve this, scalar and vector potential and gauge functions were first introduced to characterize the heat transport model. Subsequently, minimal coupling of the heat potential was established via isomorphic mapping between the heat transport and electromagnetism. The Schrödinger equation with quantized heat potentials that fulfill the gauge symmetry is established. Based upon, we further studied the quantization of enthalpy and entropy from a reversible thermodynamic process, including continuous and discretized system. Later, the connections between the non-isentropic condition and gauge symmetry violation were revealed to categorize classical-permitted and quantum-permitted processes. To support the study, thermal quantities are calculated according to the recent report in literature for the two predicted heat transport modes. Theoretically, it has been shown that the quantization of heat potentials as a consequence of isomorphic characterization and gauge symmetry. By incorporating the critical temperature and local symmetry breaking, it interprets the transition of quantum formulation to classical formulation in finite spatial and temporal limits.