Statistical physics is one of the fundamental theories of physics, and uses methods of statistics in solving physical problems. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. It can describe a wide variety of fields with an inherently stochastic nature. Stochastic (from the Greek "Στόχος" for "aim" or "guess" means Random. Examples include problems involving nuclear reactions, and topics in the fields of biology, chemistry, neurology and even some social sciences such as sociology. In Nuclear physics, a nuclear reaction is the process in which two nuclei or nuclear particles collide to produce products different from the initial particles Foundations of modern biology There are five unifying principles Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties Sociology (from Latin: socius "companion" and the suffix -ology "the study of" from Greek λόγος lógos "knowledge"
The term "statistical physics" encompasses probabilistic and statistical approaches to classical mechanics and quantum mechanics. Probability is the likelihood or chance that something is the case or will happen Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Statistical mechanics is then often used as a synonym. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics When the context requires a distinction, one uses the terms classical statistical mechanics and quantum statistical mechanics.
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. For information on degrees of freedom in other sciences see Degrees of freedom. Statistical mechanics can also describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics (particularly at high Knudsen numbers), or plasma physics. In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that Thermal physics is the combined study of Thermodynamics, Statistical mechanics, and Kinetic theory. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion The Knudsen number ( Kn) is a Dimensionless number defined as the Ratio of the molecular Mean free path length to a representative physical length In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound
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. Monte Carlo methods are a class of Computational Algorithms that rely on repeated Random sampling to compute their results