Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which 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, and neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics develop 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 classical mechanics, which is concerned with the motion of particles or objects when subjected to a force. Scope Statistical physics explains and quantitatively describes superconductivity, superfluidity, turbulence, collective phenomena in solids and plasma, and the structural features of liquid. It underlies the modern astrophysics. In solid state physics, statistical physics aids the study of liquid crystals, phase transitions, and critical phenomena. Many experimental studies of matter are entirely based on the statistical description of a system. These include the scattering of cold neutrons, X-ray, visible light, and more. Statistical physics also plays a role in materials science, nuclear physics, astrophysics, chemistry, biology and medicine (e.g. study of the spread of infectious diseases). 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, statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics. One of the most important equations in statistical mechanics (akin to in Newtonian mechanics, or the Schrödinger 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