# Questions tagged [statistical-mechanics]

The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

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### What does integrating the probability density function over all phase space gives us?

For a system of N-3D particles, we have 6N D.O.F and therefore a 6N dimensional phase space. I know that one point in phase space represents a possible state of the system. I also understand that a ...
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### Pair correlation function for non-interacting spinless bosons

While trying to solve a second quantization exercise regarding a bosonic gas, I've been having trouble trying to understand the $(1-\delta_{\text{pq}})$ term in the decomposition of the following ...
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### Interpretation of probability in Statistical Mechanics

In statistical mechanics, in particular the canonical ensemble, the probability of the system to have a particular state is given by : $$P_i=\frac{e^{-\beta E}}{Z}$$ Here $Z$ is the partition function ...
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### Exact heat capacity of the 2-dimensional Ising model

The following is a section from the book Newman, M., and G. Barkema. "Monte carlo methods in statistical physics" New York, USA (1999). and then: From those two quotes, it seems that there ...
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### Confusion regarding the use of partition function

Suppose we have a system filled with $N$ particles. There are $k$ energy levels in this system, labeled by $\epsilon_i$, each with a degeneracy of $g_i$. Let us imagine $n_j$ particles out of these $N$...
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### Quantum to classical mapping

I'm having troubles understanding precisely how the mapping from a quantum system to a classical one works. Let's say that I have a quantum system in $d$ dimensions with Hamiltonian $H$ at temperature ...