Gert's Deterministic-Geometric Model of an Ideal Gas: An Alternative Approach to Mean Free Path Calculation and a Critique of the Maxwell Distribution

Abstract:This paper investigates an alternative theoretical framework for ideal gas description based on E. Gert’s deterministic-geometric model. In contrast to the classical molecular-kinetic theory (MKT), which relies on the probabilistic-statistical apparatus of the Maxwell distribution, the proposed model quantizes the system's phase space using explicit geometric volumes ("swept cylinders") generated by rigid molecules moving discretely along six orthogonal directions. An analytical expression for the molecular mean free path is derived from pure spatial-coordinate considerations, eliminating the need for artificial semi-empirical correction factors historically used to match empirical data. From the standpoint of phenomenological thermodynamics, a critical analysis of the Maxwell distribution is presented, revealing an internal contradiction between a continuous velocity spectrum and the Second Law of Thermodynamics within an isolated, uniform equilibrium system. Finally, the prospects of applying Gert’s geometric constraints to refine the classical transport equations are outlined.