# Introduction to Mathematical Physics/Statistical physics/Introduction

Statistical physics goal is to describe matter's properties at macroscopic scale from a microscopic description (atoms, molecules, etc\dots). The great number of particles constituting a macroscopic system justifies a probabilistic description of the system. Quantum mechanics (see chapter ---chapmq---) allows to describe part of systems made by a large number of particles: Schr\"odinger equation provides the various accessible states as well as their associated energy. Statistical physics allows to evaluate occupation probabilities of a quantum state . It introduces fundamental concepts as temperature, heat\dots

Obtaining of probability is done using the statistical physics principle that states that physical systems tend to go to a state of ``maximum disorder *[ph:physt:Reif64], [ph:physt:Diu89]. A disorder measure is given* by the statistical entropy^{[1]}\index{entropy}

The statistical physics principle can be enounced as:

**Postulate:**

At macroscopic equilibrium, statistical distribution of microscopic states is, among all distributions that verify external constraints imposed to the system, the distribution that makes statistical entropy maximum.

**Remark:**

This problem corresponds to the classical minimization (or maximization) problem presented at section chapmetvar) which can be treated by Lagrange multiplier method.

- ↑ This formula is analog to the information entropy chosen by Shannon in his information theory [ph:physt:Shannon49].