Kinetic Equation and Non-equilibrium Entropy for a Quasi-two-dimensional Gas

Abstract

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function $S(t)$ is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, $S(t)$ increases monotonically in time, until the system reaches a stationary inhomogeneous state, when $S$ becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and Molecular Dynamics simulations are used to verify some of the theoretical predictions.

References in corpus (4)

• Caging dynamics in a granular fluid
• Glass Transition in Confined Geometry
• Fluids in Extreme Confinement
• Hydrodynamics for a model of a confined quasi-two-dimensional granular gas

Cited by in corpus (5)

• Kinetic theory of a confined quasi-one-dimensional gas of hard disks
• Dynamics of an inelastic tagged particle under strong confinement
• Inhomogeneous cooling state of a strongly confined granular gas at low density
• Confined granular gases under the influence of vibrating walls
• Self-diffusion in a quasi-two dimensional gas of hard spheres