The Nath-Luxuriæ principles: Unified thermodynamic framework for molecular assembly and non-ergodicity via ATP synthesis/hydrolysis example

Nath's principle posits that the maximization of free energy dissipation ($\Phi$) under specific constraints facilitates the function and assembly of complex organic molecules under specific constraints, challenging the classical view that increased dissipation leads to disorder. To ground this principle in thermodynamics, this study establishes a connection between Nath's principle and a principle applicable beyond biological systems: the Principium Luxuriæ. The latter describes how multiscale systems dissipate energy in response to external forces. The conceptual equivalence of both principles is demonstrated, supporting Nath's unified theory of ATP synthesis/hydrolysis and the existence of non-equilibrium mechanisms for cellular energy dissipation, conservation, and storage. This connection is reinforced by a mathematical relationship demonstrating a negative correlation between $\Phi$ and the thermodynamic fractal dimension ($D$), a parameter quantifying multiscale dissipation in the Principium Luxuriæ. Furthermore, a relationship is established between the equations governing homeostasis and free energy. Given that the multiscale description is predicated on constraints imposed by external forces, which limit possible molecular configurations, the non-ergodic nature of biological systems described by Nath's principle is validated. A comparative analysis is conducted, contrasting these Nath-Luxuriæ principles with Prigogine's work (which describes ergodic systems) in their application to the thermodynamic evolution of biological systems and the constraints present on Earth for the formation of life. It is suggested that the Nath-Luxuriæ principles may significantly enhance the probability of assembling complex molecules necessary for life.