Mind the Gap: Boltzmannian versus Gibbsian 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...

Mind the Gap! Abstract Versus Concrete Models of Specifications

In the theory of algebraic specifications, many-sorted algebras are used to model programs: the representation of data is arbitrary and operations are modelled as ordinary functions. The theory that underlies the formal development of programs from specifications takes advantage of the many useful properties that these models enjoy. The models that underlie the semantics of programming language...

“Mind the Gap” in Reporting the Outdated Statistics