Not exact matches
The bias is
larger for more «
macroscopic»
systems, and basically nonexistent for truly «microscopic»
systems.
They neglect the fact that thermodynamics is the valid
macroscopic heuristic for statistical mechanics, and that stat mech computations can not be done on an heuristic basis at all; they are horrendously difficult, involving taking limits of nearly infinite sums in just the right way to get the relevant part of the answer and discard the parts that don't scale up to relevance as one goes to
large systems.
All may comments are on this case and similar other cases, they are not about cases, where experiments can be repeated arbitrarily many times or were the physical
system consists of a
large number of particles that are controlled with identical constraints as the gas molecules are in a
macroscopic volume of gas.
Even for
large,
macroscopic systems, there is some infinitesimal probability that the second law could be violated.