A professional tool application integrating thermodynamics and mathematical physics. The application is built around the four core potentials of thermodynamics - internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy - and features a complete Maxwell relationship visualization module. It visually demonstrates the symmetry between thermodynamic variables through interactive thermodynamic square diagrams. Furthermore, the application delves into the frontier fields of modern mathematical physics, encompassing Legendre transformations and submanifold structures, the geometric framework of contact manifolds, thermodynamic modeling of phase transition critical phenomena, thermodynamic analysis of black hole Hawking radiation, and the geometric description of thermodynamics from the perspective of differential forms. Each module is equipped with interactive dynamic charts, real-time parameter adjustment sliders, mathematical derivation displays, and more.
