Interpretive analogies between quantum and statistical mechanics

Abstract

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology and to the quantum measurement problem.

Quantumness of States and Unitary Operations

“…Baeyer [4]) 5 ; see also Wallace [58, pp. 211-213] for the claim that the controversy concerning the meaning of probabilities in classical statistical mechanics should be resolved with the reference to quantum mechanics and McCoy [41] for the similarities in interpretative problems of quantum mechanics and classical statistical mechanics. Therefore, we have some potential ways out of our second problem, but, as previously, the issue is highly debatable.…”

Did the Universe Have a Chance?

“…There are various examples of implementing chances in this way in the foundations of quantum mechanics (Ghirardi, 2016): indeterministic behavior can happen, for example, at discrete times, as in the GRW interpretation, or continuously, as in the CSL interpretation. Other examples arise in classical statistical mechanics, especially non-equilibrium statistical mechanics (Wallace, 2014;Luczak, 2016;McCoy, 2018b).…”