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Equilibrium statistical mechanics deals much with possible configurations of a system than the governing laws of dynamics (Newton's laws in classical statistical mechanics).

My question is: to what extent Newton's laws are effective in equilibrium properties of the system? Put it in another way, if we change the laws of dynamics will we get different equilibrium properties?

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If we change the laws of dynamics we can get different equilibrium properties or not, depending on the change.

This is a well known fact for people doing numerical simulations of equilibrium properties.

On the one hand, dynamic models as different as the Newtonian, at the base of Molecular Dynamics simulations, or stochastic Monte Carlo methods may describe the same equilibrium properties, with full agreement, within the statistical error bars. On the other hand, just remaining in the realm of deterministic methods, algorithms have been developed to simulate systems under completely different equilibrium and not equilibrium conditions. For instance, the so called Nosé-Hoover thermostat corresponds to a modification of Newtonian equations of motion which allows to generate dynamical trajectories such that the mechanical energy is not conserved but time averages provide a statistical distribution of the values of observable quantities in agreement with the canonical ensemble.

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