Inelastic collisions as a source of entropy?

TL;DR

This paper explores whether inelastic collisions in gases and liquids can be a fundamental source of entropy production, linking microscopic quantum processes with macroscopic thermodynamic behavior through theoretical models and potential experimental verification.

Contribution

It introduces a quantum two-state model for inelastic collisions that predicts entropy production and thermal relaxation, proposing a new perspective on the microscopic origins of entropy beyond chemical reactions.

Findings

Master equations yield entropy production and equilibration in translational degrees

Predicted relaxation rates depend on activation energy and process order

Temperature dependence aligns with activation energy of transitions

Abstract

Activation/deactivation by inelastic collisions have been extensively studied at unimolecular reactions in gas phase where they are crucial for equilibration. As equilibration means an increase of entropy, the mechanism can also be considered responsible for entropy production. Theoretical treatments show a remarkable agreement with experiments. They rest upon the assumption of stochastic quantum transitions. Under this premise, master equations have been used that are known to deliver equilibria and entropy production. Here we examine the hypothesis that the ubiquitous inelastic interactions in gas and liquid phase may represent a source of entropy beyond chemical reactions, rotational activation/deactivation being the prevailing mechanism in gas dynamics at room temperature. For a quantum mechanical two-state model the master equations are formulated which yield entropy production and equilibration in translational degrees of freedom until, at conserved energy, a stationary Maxwell-Boltzmann distribution is reached. The relaxation rates show features that can be checked by monitoring thermal relaxation in gas phase. Depending on the composition, first or second order processes are predicted. The temperature dependence is determined by the activation energy of the lowest transition. Thus, experimental verification will allow to decide to which extent this hypothesis describes thermal relaxation. It would support a connection between the macroscopic second law of thermodynamics and the microscopic stochastic collapse in quantum mechanics, both experimentally secured facts which in theory emerge as special elements beyond Hamiltonian dynamics. It is also shown that inelastic collisions are connected with velocity-dependent forces and result in a new analog of the Fokker-Planck equation where they replace Langevin dynamics as a non-Hamiltonian dissipative mechanism.