Maximum Entropy Thermodynamics - Philosophical Implications - The Nature of The Probabilities in Statistical Mechanics

The Nature of The Probabilities in Statistical Mechanics

Jaynes (1985, 2003, et passim) discussed the concept of probability. According to the MaxEnt viewpoint, the probabilities in statistical mechanics are determined jointly by two factors: by respectively specified particular models for the underlying state space (e.g. Liouvillian phase space); and by respectively specified particular partial descriptions of the system (the macroscopic description of the system used to constrain the MaxEnt probability assignment). The probabilities are objective in the sense that, given these inputs, a uniquely defined probability distribution will result, independent of the subjectivity or arbitrary opinion of particular persons. The probabilities are epistemic in the sense that they are defined in terms of specified data and derived from those data by definite and objective rules of inference. Here the word epistemic, which refers to objective and impersonal scientific knowledge, is used in the sense that contrasts it with opiniative, which refers to the subjective or arbitrary beliefs of particular persons; this contrast was used by Plato and Aristotle and stands reliable today.

The probabilities represent both the degree of knowledge and lack of information in the data and the model used in the analyst's macroscopic description of the system, and also what those data say about the nature of the underlying reality.

The fitness of the probabilities depends on whether the constraints of the specified macroscopic model are a sufficiently accurate and/or complete description of the system to capture all of the experimentally reproducible behaviour. This cannot be guaranteed, a priori. For this reason MaxEnt proponents also call the method predictive statistical mechanics. The predictions can fail. But if they do, this is informative, because it signals the presence of new constraints needed to capture reproducible behaviour in the system, which had not been taken into account.