Are Boltzman's statistics compatible with deterministic universe? Suppose that the gas molecules in a given container are perfectly elastic objects obeying Newton's laws. Suppose further that we select the initial conditions (impulse and position of each molecule) at random. Is it true that, if the initial conditions are randomly selected, then in most cases the entropy will be increasing (but in some cases it will not)? Or do Boltzman's statistics imply inherent indeterminism/uncertainty at some level, i.e. the quantum level?