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In physics, thermalisation (or thermalization) is the process of physical bodies reaching thermal equilibrium through mutual interaction. In general, the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system's entropy .
The classical Stefan problem aims to describe the evolution of the boundary between two phases of a material undergoing a phase change, for example the melting of a solid, such as ice to water. This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions.
The original intent was to find a physics problem worthy of numerical simulation on the then-new MANIAC computer. Fermi felt that thermalization would pose such a challenge. As such, it represents one of the earliest uses of digital computers in mathematical research; simultaneously, the unexpected results launched the study of nonlinear systems.
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields: Natural sciences, engineering and medicine
Quark–gluon plasma is a state of matter in which the elementary particles that make up the hadrons of baryonic matter are freed of their strong attraction for one another under extremely high energy densities. [22]
The problem has a solution; The solution is unique; The solution's behavior changes continuously with the initial conditions; Examples of archetypal well-posed problems include the Dirichlet problem for Laplace's equation, and the heat equation with specified initial conditions. These might be regarded as 'natural' problems in that there are ...
Examples of this would include the occupation of a given momentum in a gas of particles, [4] [5] or the occupation of a particular site in a lattice system of particles. [5] Notice that while the ETH is typically applied to "simple" few-body operators such as these, [ 4 ] these observables need not be local in space [ 5 ] - the momentum number ...
This process of "quantum thermalization" may be understood in terms of B acting as a reservoir for A. In this perspective, the entanglement entropy S = − Tr ( ρ A log ρ A ) {\displaystyle S=-\operatorname {Tr} (\rho _{A}\log \rho _{A})} of a thermalizing system in a pure state plays the role of thermal entropy.