# Metropolis Algorithm and integration volume

1. Jun 22, 2012

### Derivator

Hello,

the Metropolis algorithm can be used to evaluate canonical expectation value integrals by sampling from the Boltzmann density. In the canonical ensemble, one has a finite and constant volume V, over which the configurational part of the expectation-value integral is integrated over.

However, in all descriptions and implementations of the Metropolis-Algorithm, I have never seen that such a volume restriction is obeyed. Everybody just seems to assume that the simulated particles can move freely in an infinite volume. Could someone explain, why one obtains correct results, despite not obeying finite volume constraints? Is this, because the simulation can (in practice) only be executed for a finite time, and hence it will only cover a finite (but large) volume (and this volume, because it is still finite, is canceled by the normalization of the expectation value).

Best,
derivator

2. Jun 23, 2012