Boundary value problems (BVP) are a robust mathematical framework that describes and solves challenging physical phenomena in various scientific areas. BVPs are critical in understanding and modeling a wide range of phenomena in thermodynamics and kinetics, from heat transfer and phase transitions to chemical reactions and reaction rates. In the context of BVP in thermodynamics and kinetics, we introduce a mathematical framework to describe thermodynamic processes occurring in deformable systems. This framework includes the influence of dissipative effects on the development of near-surface phenomena. Expressions describing the local state (LS) and the description of dissipative processes (DP) can be derived by integrating kinetic energy and applying thermodynamic principles. Furthermore, utilizing the variational approach, we can builds a function, when minimized, that provides those connections relating to the LS, the description and the application of natural boundary conditions. We explain the requisite conditions for the convexity of this function.

Thermodynamics, Kinetics, Boundary value problem (BVP), Local and Variational Formulation