The main purpose of this paper is to show that it is possible to understand the origin of irreversibility with a simple one-dimensional model of a collisionless gas. We begin by studying a one-particle "gas" and then we generalise the results to an N-particle gas. The gas particles are enclosed in a cylinder and their movement is perpendicular to a frictionless piston. Only elastic collisions of the particles with the cylinder bottom and the piston are consider. In order to understand the origin of irreversibility we compare the solution obtained for the differential equation f=dp/dt, where the force f on the piston is due to the gravitational field and to the particle collisions on the piston, with the solution obtained for the momentum conservation law. When the number of particles increases and are not in phase, both solutions must agree most of the time in agreement with a statistical formulation. Therefore irreversibility exists in a model without friction between the piston and the cylinder wall and without heat flux between the gas and the exterior. And, although this is commonly suggested, it is not due to mathematical hypothesis like the use of a mean value for the force due to the particle collisions. In fact irreversibility has its origin in the interaction between the particles through the piston and then the statistical formulation agree with am exact and deterministic solution, most of the time and for most of the initial conditions, but not for all time and all the initial conditions.
Comments: 27 Pages. EPS 10 TRENDS IN PHYSICS 10th General Conference of the European Physica Society, Abstracts p. 314 (1996)
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