But when we apply statistical mechanics to "microscopic" arrangments like a few particles in an idealized rigid box or in a vacuum, there is no arrow of time. T

But when we apply statistical mechanics to "microscopic" arrangments like a few particles in an idealized rigid box or in a vacuum, there is no arrow of time. The laws of physics themsleves are totally symmetric (CPT theorem), and it is not thought the t-asymmetry of the weak interaction is responsible for the global macroscopic arrow of time. So without some statement of initial/prior conditions, we have no reason to see just the "forward" arrow unless we say something about initial/prior conditions. (Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox)