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Résumé |
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations
of motion are
time reversal invariant. One objection to irreversibility is based on Poincare's recursion theorem: a classical Hamiltonian
confined system
returns after some time, so-called Poincare recurrence time (PRT), close to its initial configuration. Boltzmann's reply was
that for a
$N \sim 10^{23} $ macroscopic number of particles, PRT is very large and exceeds the age of the universe. In this paper
we compute for the
first time, using molecular dynamics, a typical recurrence time $T(N)$ for a realistic case of a gas of $N$ particles.
We find that $T(N) \sim N^z \exp (y N) $ and determine the exponents $y$ and $z$ for different values of the particle
density and
temperature. We also compute $y$ analytically using Boltzmann's hypotheses. We find an excellent agreement with the
numerical results.
This agreement validates Boltzmann's hypotheses, not yet mathematically proven. We establish that $T(N) $ exceeds the
age of the
Universe for a relatively small number of particles, much smaller than $ 10^{23} $.
Joint work with Dominique Levesque |
