A simple probabilistic model of ideal gases. (English) Zbl 1352.82010

The present paper is devoted to an attempt to construct a three-dimensional discrete model of the thermodynamics of ideal gases based on a probabilistic definition of the microstates of the gas. The author assumes that the particles move randomly (as in ASEP models) instead of obeying Newton’s laws as prescribed by Boltzmann. It is established that the model eventually reaches a “fluctuating equilibrium” independently of the initial conditions, i.e., the macroscopic variables stabilize in the sense that they perform very small fluctuations near certain constant values. Moreover, the author shows that the particles satisfy the classical laws of ideal gases. It is observed that once fluctuating equilibrium is achieved, the number of moving particles becomes a fluctuating constant and, hence, the macroscopic variables – the energy, the temperature \(T\), and the pressure also become fluctuating constants. The author also studies the behavior of different versions of the defined model in different situations such as evaporation, condensation, compression, heating and cooling.


82B40 Kinetic theory of gases in equilibrium statistical mechanics
82D05 Statistical mechanics of gases
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