Abstract :
It is sometimes stated that in order to be amenable to a simple statistical description, a system needs to have many coupled degrees of freedom. In this view, the statistical limit is to be understood from the dynamics. Here we discuss a complementary point of view where the role of ‘size’ is to ensure that the probabilities of simple events, which are technically marginal probabilities, settle down to a canonical distribution, conditioned by additive constants of the motion. The requirement that the conditioning is on additive variables plays an essential technical role and it is not clear that this condition can be relaxed. In the view discussed here, the effective ‘size’ is determined by the variance of the physical variables of interest. Implications for Monte Carlo sampling are also discussed, with examples.
