Statistical Physics - Statistical Mechanics

Statistical Mechanics

Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics, classical mechanics, and quantum mechanics at the microscopic level. Because of this history, the statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics.

One of the most important equations in Statistical mechanics (analogous to in mechanics, or the Schroedinger equation in quantum mechanics ) is the definition of the partition function, which is essentially a weighted sum of all possible states available to a system.

where is the Boltzmann constant, is temperature and is energy of state . Furthermore, the probability of a given state, occurring is given by

Here we see that very-high-energy states have little probability of occurring, a result that is consistent with intuition.

A statistical approach can work well in classical systems when the number of degrees of freedom (and so the number of variables) is so large that exact solution is not possible, or not really useful. Statistical mechanics can also describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics (particularly at high Knudsen numbers), or plasma physics.

Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions. A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the dynamics of a complex system.