| This essay explores the philosophical issues concerning the interpretation of probabilities in the context of equilibrium classical statistical mechanics. One reason why investigators have never settled on a single interpretation of probability is that different theories seem to demand different concepts of probability. For example, quantum physics seems to demand an ontic "propensity" concept of probability, while decision theory demands an epistemic "personalist" concept of probability. Statistical mechanics is a branch of physics which uses probabilities to enable experimenters to make predictions in spite of ignorance of the exact microstates of (deterministic) systems. It therefore seems to demand a "mixed" concept of probability that has both ontic and epistemic aspects. For this reason, analyzing probabilities in statistical mechanics can be expected to shed light on the general philosophical problems surrounding the interpretation of probability.; ET Jaynes has offered a theory of statistical mechanics, called "predictive statistical mechanics" [PSM] that uses the "maximum entropy" (maxent) principle to justify the probability distributions used in statistical mechanics. Because the maxent principle is a general principle of Bayesian statistical inference, probabilities in PSM are naturally interpreted in epistemic terms.; Solutions are proposed to the two conceptual problems that have prevented PSM from gaining widespread acceptance. First, it is pointed out that the uniform measure is (up to an irrelevant constant) the unique measure that is preserved by the class of local canonical transformations of phase space. This fact provides a certain justification for the use of the uniform measure as the "background" or "prior" measure needed to apply the maxent principle to statistical mechanics.; Second, it is suggested that maxent constraints should be interpreted in terms of Fisher's concept of sufficiency. This interpretation leads to a certain justification of the maxent rule. In addition, it brings PSM in line with a "phonomenological" theory of statistical mechanics developed by Benoit Mandelbrot in the late 1950's. Besides putting PSM on a firmer theoretical foundation, these amendents clarify two points at which this theory's "subjective" probabilities are endowed with physical significance. |
