Maxwell & Gibbs: 150 Years since the Foundations of Statistical Mechanics

This talk will demonstrate the importance of the historical and conceptual foundations of statistical mechanics by mapping out different derivational routes to the Arrow of Time. It will demonstrate that there are at least three different derivational routes: (i) starting from the Thermodynamic Entropy and inductively deriving the Empirical 2nd Law to ground the Empirical Arrow of Time; (ii) starting from a notion of randomness, which acts as a desiderata on the definition of Boltzmann and Gibbs Entropy, from which one can deductively derive the Statistical 2nd Law and then ground either (ii) the Universal Statistical Arrow of Time, or (iii) the Local Statistical Arrow of Time. Each of the three Arrows has different epistemic advantages and disadvantages: prominently, the Empirical Arrow of Time provides a straightforward definitional grounding of the direction of time; in contrast, the two statistical Arrows of Time have higher explanatory potentials, but their derivation requires the introduction of additional assumptions.