Statistical Mechanics and Scientific Explanation Determinism, Indeterminism and Laws of Nature

Boltzmann showed how the phenomenological laws of thermodynamics, such as the second law of thermodynamics, can be suitably derived from statistical mechanics, which is based on classical mechanics. What exactly does this explanation amount to?
Assuming that Boltzmann is able to explain the thermodynamic arrow of time connected with the second law, what about the psychological arrow?
Many physicists use the notion of typicality instead of the one of probability when discussing statistical mechanics. What is typicality? What is its connection with probability? Is typicality explanatory?
How can one extend Boltzmann's analysis to the quantum domain? Can indeterminism help or it does not play a fundamental role?
How does this approach extend to theories in which gravity plays an important role?
Boltzmann's explanation fundamentally involves cosmology: for the explanation to go through the Big Bang needs to have had extremely low entropy. Does the fact that the Big Bang was a low entropy state imply that it was, in some sense, "highly improbable" and requires an explanation? Are there approaches in which one can avoid postulating something like the past hypothesis?
Statistical mechanics has two main formulations: one due to Boltzmann and the other due to Gibbs. What is the connection between the two formulations? Is one more fundamental than the other?
Readership: Graduate and research level students and professional in mathematical physics, statistical mechanics, quantum theory and physics.


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