# Boltzmann

## The Microcanonical Ensemble

The microcanonical ensemble is a probability space which models physical systems at a fixed energy. We imagine a physical system whose states are described by some set $\Omega$ (which we will assume is a measurable… Read More »The Microcanonical Ensemble

## The Canonical Ensemble

The canonical ensemble is a probability space which models physical systems at a fixed temperature, but for which the energy can vary. In this situation we imagine that our system, described by states \$(\Omega, \mathcal… Read More »The Canonical Ensemble

## The Grand Canonical Ensemble

The grand canonical ensemble is a probability space which models physical systems with a variable number of particles and variable energy at a fixed temperature. Here we imagine our physical system is in contact with… Read More »The Grand Canonical Ensemble

## Two-Dimensional Electrostatics

In two dimensional electrostatics we imagine infinite parallel wires in three dimensions carrying specified charge densities. By inserting a plane perpendicular to the charged wires we may identify each wire with its intersection point in… Read More »Two-Dimensional Electrostatics