Statistical mechanics

The statistical mechanics was originally a field of application of mechanics. Nowadays, the term is often used synonymously with the statistical physics and statistical thermodynamics and thus stands for the ( theoretical and experimental ) analysis of numerous, fundamental properties of systems of many particles (atoms, molecules, etc. ). Inter alia provides statistical mechanics, a microscopic foundation of thermodynamics. It is therefore of great importance for the chemical industry, especially for Physical Chemistry, in which one speaks of statistical thermodynamics.

In addition, it describes a plurality of further thermal equilibrium and non-equilibrium properties (e.g., scattering experiments ) were investigated with the aid of modern measuring techniques.

In the ( initial ) random mechanical condition of a physical system is not characterized by the trajectory, i.e., by the time curve of locations and pulses of the individual particles or the quantum states, but the probability to be found such microscopic conditions.

The statistical mechanics is developed especially by the work of James Clerk Maxwell, Ludwig Boltzmann and Josiah Willard Gibbs, the latter coined the term. Below are some concepts from statistical physics are explained, which play an important role especially in the analysis of properties of thermal equilibrium.

Historically, of central importance is the Boltzmann's entropy formula (which is also engraved on the grave stone of Ludwig Boltzmann ):

Here S denotes the (statistical ) entropy of a closed system, ie a microcanonical ensemble. The size is the number of microstates (for example, positions and momenta of all particles in a gas ) that are compatible with the thermodynamic state variables energy, volume and number of particles ( Boltzmann described this size as " Komplexionzahl " equal to the statistical weight, sometimes specified as W, the macroscopic state ). The constant is called the Boltzmann constant, and how the entropy unit Joules per Kelvin.

It is therefore considered that not a single microscopic state, but rather all possible states determine the macroscopic behavior of a physical system. Statistical ensembles play a crucial role in statistical physics; a distinction between the microcanonical, canonical and grand canonical ensemble.

A classical and easy example of the application of the statistical mechanics, the derivation of the equation of state of an ideal gas and the Van der Waals gas.

Are quantum properties ( indistinguishability of the particles ) is essential, for example, at low temperatures, can special phenomena occur and can be predicted from statistical physics. For systems with integer spin ( bosons ) the Bose -Einstein statistics apply. Below a critical temperature and at a sufficiently weak interactions between the particles occurs, a special effect in which a plurality of particles to the lowest energy state occupy: There is a Bosekondensation.

Systems with half-integer spin ( fermions ) obey the Fermi -Dirac statistics. Because of the Pauli principle also states of higher energy are accepted. There is a characteristic upper " edge energy ", the Fermi energy. It determines, inter alia, numerous thermal properties of metals and semiconductors.

The concepts of statistical mechanics can be applied not only on the position and momentum of the particles but also on others, such as magnetic properties. Here, the modeling is of great importance; For example, reference is made to the detail examined Ising model.