 # Statistical Physics

Statistical physics is the holy grail of Physics. It has taught us a great many lessons in the universe and will definitely teach us more. Statistical physics aims at studying the macroscopic parameters of a system in equilibrium from the knowledge of the microscopic properties using the law of mechanics. This approach is different from thermodynamics that studies the macroscopic system in equilibrium from the macroscopic standpoint without considering the microscopic parameters.

Statistical physics can be defined as,

The branch of physics where a scheme to calculate the free energy is formulated. In statistical physics, we use the fact that matter consists of atoms. On the basis of a knowledge of the microscopic laws that govern the motion of atoms and most importantly an additional law of statistical physics, it gives a general expression for the free energy.

Statistical physics can study both thermal equilibrium states and non-equilibrium states.

## Why do we need a statistical description?

Statistics used in physics render a conceptual link between the macroscopic and the microscopic view. For example, when studying gases, we can examine the statistical distribution of particle velocities and gain an understanding of the relationship between the macroscopically observable quantities such as the pressure, volume, and temperature. Given below in a table, are a few of its applications:

 Maxwell-Boltzmann statistics are used to describe the distribution of particles at different energy levels as a function of temperature. This has can be used to gain insight into a wide range of processes such as diffusion. Applying a statistical approach to thermodynamics can furnish a deeper understanding of concepts such as entropy. For instance, the temperature can be understood statistically, as the average kinetic energy of atoms in a bulk material. The application of statistics to describe processes such as Brownian motion has proven to be useful in the derivation of the ‘path-integral’ formulation of quantum physics. On a broader level, the study of statistics provides a practical set of tools for testing hypotheses and estimating confidence intervals on aggregate data, not only in Physics but in all the scientific disciplines. In this sense, it forms the basis for the proper design of experiments, interpretation (significance) of data and correlation of information which ultimately underpins the development of modern scientific knowledge.

### Application of Statistical Physics

Following are the statistical physics applications:

• The first statistical physics application was concentrated on the distribution of molecules in an assembly. It was applied in Maxwell’s distribution of molecular velocity.
• Gibb’s explained the thermodynamics with the help of statistical physics. 