We introduce a high-dimensional
symplectic map, modeling a large
system, to analyze the interplay between single-particle chaotic
dynamics and particles interactions in thermo
dynamic systems. We study the initial growth of the Boltzmann entropy,
SB, as a function of the coarse-graining resolution (the late stage of the evolution is trivial, as the
system is subjected to no external drivings). We show that a characteristic scale emerges, and that the behavior of
SB vs
t, at variance with the Gibbs entropy, does not depend on the resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth, in its early stage, depends essentially on the single-particle chaotic
dynamics. It is possible to interpret the basic features of the
dynamics in terms of a suitable Markov approximation.