A Field Guide to Recent Work on the Foundations of Statistical Mechanics

Statistical mechanics (SM) is the study of the connection between micro-physics and macro-physics. 1 Thermodynamics (TD) correctly describes a large class of phenomena we observe in macroscopic systems. The aim of statistical mechanics is to account for this behaviour in terms of the dynamical laws governing the microscopic constituents of macroscopic systems and probabilistic assumptions. 2 This project can be divided into two sub-projects, equilibrium SM and non-equilibrium SM. This distinction is best illustrated with an example. Consider a gas initially confined to the left half of a box (see fig. 3.1): Fig. 3.1. Initial state of a gas, wholly confined to the left compartment of a box separated by a barrier This gas is in equilibrium as all natural processes of change have come to an end and the observable state of the system is constant in time, meaning that all macroscopic parameters such as local temperature and local pressure assume constant values. Now we remove the barrier separating the two halves of the box. As a result, the gas is no longer in equilibrium and it quickly disperses (see fig. 3.2): This process of dispersion continues until the gas homogeneously fills the entire box, at which point the system will have reached a new equilibrium state (see fig. 3.3):