Dynamic anisotropy of degrees of freedom in nonequilibrium thermodynamics: kinematic failure of the energy equipartition theorem

Abstract:This paper presents a critical analysis of the Maxwell-Boltzmann equipartition theorem within the framework of pre-relaxation physical kinetics. Based on the laws of classical Newtonian mechanics, binary collisions of polyatomic molecules of arbitrary configuration and their interaction with a solid boundary are investigated. The existence of a spatial-geometric asymmetry of energy transfer is demonstrated, revealing a "one-way valve" effect under the kinematic condition where the internal (rotational-vibrational) velocity exceeds the translational velocity of the molecule's center of mass (\(v < R\omega\)). Building upon the molecular-kinetic theory (MKT), a generalized formula for the adiabatic index is derived, accounting for the half-energy contribution of non-translational degrees of freedom. This mathematical framework consistently explains the experimental values of the adiabatic index across a wide temperature range without the artificial "freezing" of vibrational, torsional, or shear modes. Furthermore, a thermodynamic mechanism is substantiated for harnessing the total internal energy accumulated in passive degrees of freedom to perform macroscopic work via the directional channeling of molecular momentum.