Simulations is a tool to try to understand the origin irreversibility, the asymmetry between past and future. However, the fluctutions in finite systems and the noise in the integration algorithms limits the possibility to use simulations to study the origin of thermodynamic behaviour.
The status of models to explain the origin of the second law of thermodynamics
in Hamiltonian systems is
Ergodicity: The math does not work.
Quasi-ergodicity: Does not guarantee the
existence of an eqilibrium.
Metric indecomposability:
Necessecary and sufficient for existence of equilibrium.
Mixing:
The entropy is constant.
Coarse graining:
Does not generate asymmetry between past and future.
Forming the trace: Gives the correct
form of the second law.
Asymmetry in the initial conditions:
Gives the correct
form of the second law.