Editing Dissipation (section)

== Definition ==
Dissipative thermodynamic processes are essentially irreversible because they [[entropy production|produce entropy]]. [[Max Planck|Planck]] regarded friction as the prime example of an irreversible thermodynamic process.<ref>[[Max Planck|Planck, M.]] (1926). "Über die Begründung des zweiten Hauptsatzes der Thermodynamik", ''Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl.'', 453—463.</ref> In a process in which the temperature is locally continuously defined, the local density of rate of entropy production times local temperature gives the local density of dissipated power.{{Definition needed|date=July 2021}}

A particular occurrence of a dissipative process cannot be described by a single individual [[Hamiltonian mechanics|Hamiltonian]] formalism. A dissipative process requires a collection of admissible individual Hamiltonian descriptions, exactly which one describes the actual particular occurrence of the process of interest being unknown. This includes friction and hammering, and all similar forces that result in decoherency of energy&mdash;that is, conversion of [[Coherence (physics)|coherent]] or directed energy flow into an indirected or more [[isotropic]] distribution of energy.

=== Energy ===
"The conversion of mechanical energy into heat is called energy dissipation." – ''François Roddier''<ref>[http://www.editions-parole.net/?product=thermodynamique-de-levolution-un-essai-de-thermo-bio-sociologie Roddier F., ''Thermodynamique de l'évolution (The Thermodynamics of Evolution)'', parole éditions, 2012]</ref> The term is also applied to the loss of energy due to generation of unwanted heat in electric and electronic circuits.

=== Computational physics ===
In [[computational physics]], numerical dissipation (also known as "[[Numerical diffusion]]") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. When the pure [[advection]] equation, which is free of dissipation, is solved by a numerical approximation method, the energy of the initial wave may be reduced in a way analogous to a diffusional process. Such a method is said to contain 'dissipation'. In some cases, "artificial dissipation" is intentionally added to improve the [[numerical stability]] characteristics of the solution.<ref>Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)</ref>

=== Mathematics ===
A formal, mathematical definition of dissipation, as commonly used in the mathematical study of [[measure-preserving dynamical system]]s, is given in the article ''[[wandering set]]''.