physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, thermalisation is the process of physical bodies reaching

thermal equilibrium Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be i ...

through mutual interaction. In general the natural tendency of a system is towards a state of

equipartition of energy In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. ...

and uniform

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...

that maximizes the system's

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

. Thermalisation, thermal equilibrium, and temperature are therefore important fundamental concepts within

statistical physics 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 Mathematics, mathematical tools for dealing with large populations ...

statistical mechanics 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 be ...

, and

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

; all of which are a basis for many other specific fields of scientific understanding and engineering application. Examples of thermalisation include: * the achievement of equilibrium in a plasma. * the process undergone by high-energy neutrons as they lose energy by collision with a moderator. The hypothesis, foundational to most introductory textbooks treating

quantum statistical mechanics Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator ''S'', which is ...

, assumes that systems go to thermal equilibrium (thermalisation). The process of thermalisation erases local memory of the initial conditions. The

eigenstate thermalisation hypothesis The eigenstate thermalization hypothesis (or ETH) is a set of ideas which purports to explain when and why an isolated Quantum mechanics, quantum mechanical system can be accurately described using equilibrium statistical mechanics. In particular ...

is a hypothesis about when quantum states will undergo thermalisation and why. Not all quantum states undergo thermalisation. Some states have been discovered which do not (see below), and their reasons for not reaching thermal equilibrium are unclear .

Theoretical description

The process of equilibration can be described using the

H-theorem In classical statistical mechanics, the ''H''-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity ''H'' (defined below) in a nearly-ideal gas of molecules. L. Boltzmann,Weitere Studien über das Wä ...

or the relaxation theorem, see also

entropy production Entropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic d ...

Systems resisting thermalisation

Some such phenomena resisting the tendency to thermalize include (see, e.g., a

quantum scar Quantum scarring refers to a phenomenon where the eigenstates of a classically chaotic quantum system have enhanced probability density around the paths of unstable classical periodic orbits. The instability of the periodic orbit is a decisive p ...

): * Conventional quantum scars, which refer to eigenstates with enhanced probability density along unstable periodic orbits much higher than one would intuitively predict from classical mechanics. * Perturbation-induced quantum scarring: despite the similarity in appearance to conventional scarring, these scars have a novel underlying mechanism stemming from the combined effect of nearly-degenerate states and spatially localized perturbations, and they can be employed to propagate quantum wave packets in a disordered quantum dot with high fidelity. * Many-body quantum scars. *

Many-body localisation Many-body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems. It is characterized by the system failing to thermalization, reach thermal equilibrium, and retaining a memory of its initial condition in lo ...

(MBL), quantum many-body systems retaining memory of their initial condition in local observables for arbitrary amounts of time. Other systems that resist thermalisation and are better understood are quantum

integrable In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...

systems and systems with

dynamical symmetries In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a ...

References

Thermodynamics {{Quantum-stub