# The ideal thermometer

## Introduction

Consider an extra degree of
freedom called the *demon* which exchanges energy with a system consisting of many particles (spins). The demon exchanges energy with the system by choosing a particle (spin) at random and making a random change in its relevant coordinate. If the energy change of the system is negative, the "extra" energy is given to the demon and the trial change is accepted. If the energy change of the system is positive, the trial change is accepted if the demon has sufficient energy to give to the system. The only constraint is that E_{d}, the energy of the demon, must be greater than or equal to zero; otherwise, the trial change is not accepted.

The total energy of the demon plus
the system is fixed. The demon can trade energy with the system as long as
the demon's energy remains greater than zero.

- Ideal gas. Simulation of a demon exchanging energy with an ideal gas of particles. Illustrates that the demon can be interpreted as an ideal thermometer.
- Einstein solid. Simulation of a demon exchanging energy with an Einstein solid. The main purpose is to show that the demon energy distribution is universal and has the same form as for the ideal gas.
- Lennard-Jones fluid. A simulation of a demon exchanging energy with a system of particles in two dimensions interacting with the Lennard-Jones potential.

Updated 20 March 2020.