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The introduction of a discrete space-time represents an attempt to describe the physics at the Planck's scale. We show that this concept can be also very useful in describing thermodynamics in a pre-relativistic world. From this concept a new approach of statistical mechanics based on a dynamic viewpoint and an entropy representation is presented. The entropy is connected with the counting of the paths in space-time. It contains a time interval that represents the time that we have to wait in order to relax the quantum fluctuations and to reach the thermal regime. It is shown that this time is β hbar. The mathematical expressions we derive for thermal quantities like the entropy and the free energy are identical to those obtained by the traditional path-integral formalism starting from the canonical form of the thermal density matrix. However, the introduction of a quantized space-time shows that thermodynamics is consistent with an equation of motion that is time-irreversible at a microscopic level. As a consequence, the problem of irreversibility is revisited and the derivation of a H-theorem becomes possible in the future

STATISTICAL MECHANICS IN A DISCRETE SPACE-TIME. THERMODYNAMICS AND TIME-IRREVERSIBILITY