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A kinetic equation for a dilute gas of hard spheres confined between twoparallel plates separated a distance smaller than two particle dimeters isderived. It is a Boltzmann-like equation, which incorporates the effect of theconfinement on the particle collisions. A function $S(t)$ is constructed byadding to the Boltzmann expression a confinement contribution. Then it is shownthat for the solutions of the kinetic equation, $S(t)$ increases monotonicallyin time, until the system reaches a stationary inhomogeneous state, when $S$becomes the equilibrium entropy of the confined system as derived fromequilibrium statistical mechanics. From the entropy, other equilibriumproperties are obtained, and Molecular Dynamics simulations are used to verifysome of the theoretical predictions.

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