Statistical physics

Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neuroscience, and even some social sciences, such as sociology and linguistics. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neuroscience, and even some social sciences, such as sociology and linguistics. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. In particular, statistical mechanics develops the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. 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, statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics. One of the most important equations in statistical mechanics (analogous to F = m a {displaystyle F=ma} in Newtonian mechanics, or the Schrödinger equation in quantum mechanics) is the definition of the partition function Z {displaystyle Z} , which is essentially a weighted sum of all possible states q {displaystyle q} available to a system. where k B {displaystyle k_{B}} is the Boltzmann constant, T {displaystyle T} is temperature and E ( q ) {displaystyle E(q)} is energy of state q {displaystyle q} . Furthermore, the probability of a given state, q {displaystyle q} , occurring is given by