A geometrical theory of thermal phenomena based on the kernel of the evolution equation

Abstract: The kernel of the evolution equation is used to build a mathematical theory of thermal phenomena of gaseous and condensed matter. The group velocity of sound and the molar density are proposed to be its two thermal variables that replace the over-complete set of temperature, pressure and volume. The defining constants of the New SI (2019) of physical units are used to form a dimensionless variable of the new geometrical thermal theory. The dimensionless thermal sum generates, by the variation principle, equations on physical observables. Energy and entropy are neither defined nor needed in the present formalism. The molar specific heat is derived and its temperature dependence is verified with the experimental data for mono-atomic gases. Critique of the postulates and notions of traditional statistical thermodynamics is given.