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Concept# Statistical mechanics

Summary

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.
Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.
Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions.
The founding of the field of statistical mechanics is generally credited to three physicists:
Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates
James Clerk Maxwell, who developed models of probability distribution of such states
Josiah Willard Gibbs, who coined the name of the field in 1884
While classical thermodynamics is primarily concerned with thermodynamic equilibrium, statistical mechanics has been applied in non-equilibrium statistical mechanics to the issues of microscopically modeling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions and flows of particles and heat. The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study the simplest non-equilibrium situation of a steady state current flow in a system of many particles.
In 1738, Swiss physicist and mathematician Daniel Bernoulli published Hydrodynamica which laid the basis for the kinetic theory of gases.

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