Rethinking Boltzmannian Equilibrium

Rethinking Boltzmannian Equilibrium

Boltzmannian statistical mechanics partitions the phase space into macroregions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maximum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macros...

When Does a Boltzmannian Equilibrium Exist?

6 Gases 19 6.1 The Dilute Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6.2 The Ideal Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6.3 The Kac Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6.4 Gas of Noninteracting Particles in a Stadium-Box . . . . . . . . . . . 25 6.5 Gas of Noninteracting Particles in a Mushroom-Box . . . . ...

Typicality and the Approach to Equilibrium in Boltzmannian Statistical Mechanics

Systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium. Why do they do so? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such and not clearly distinguished. The aim of...

Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence

In Boltzmannian statistical mechanics macro-states supervene on microstates. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting b...

Probability in Boltzmannian Statistical Mechanics