# Demon Monte Carlo Models

The Lennard-Jones Demon model uses the demon Monte Carlo algorithm to simulate n particles interacting through the Lennard-Jones potential. A Monte Carlo method is a stochastic (nondeterministic) algorithm that uses random numbers to sample the microcannonical ensemble. The microcanonical ensemble is a large number number of systems with the same energy each of which represents a possible state of the actual system.

A Monte Carlo demon is an extra degree of freedom that is allowed to transfer energy as it attempts to change the state of the system. The demon keeps track of its own energy and can take or give energy to a particle as it interacts with a randomly chosen particle. Because the demon cannot have negative energy, the total energy of the system remains constant -- as it should in the microcanonical ensemble. The demon is, in effect, a thermometer. Its extra degree of freedom perturbs the system very little and the average demon energy is proportional to the temperature of the system. (See Statistical and Thermal Physics notes by H. Gould and J. Tobochnik.)

Simple Monte Carlo methods become inefficient (or fail) if they do not sample all possible configurations (phase space). The Lennard-Jones Demon model shows snapshots of phase space sampled by the demon algorithm. Do the snapshots in this simulation suggest that demon is able to sample all of phase space at high temperature? Low temperature?

### Related Models

See the Lennard-Jones Metropolis model for similar model that uses the Metropolis Monte Carlo algorithm.

### Note:

This simulation was created by Wolfgang Christian using the Easy Java Simulations (Ejs) modeling tool. You can modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu. Information about Ejs is available at: <http://www.um.es/fem/Ejs/>.