Editing Dissipation

{{short description|Irreversible transformation of energy into forms less capable of doing work}}
{{redirect|Dissipative|the mathematical term|Dissipative operator}}
In [[thermodynamics]], '''dissipation''' is the result of an [[irreversible process]] that affects a [[thermodynamic system]]. In a dissipative process, [[energy]] ([[Internal energy|internal]], bulk flow [[Kinetic energy|kinetic]], or system [[Potential energy|potential]]) [[Energy transformation|transforms]] from an initial form to a final form, where the capacity of the final form to do [[Work (thermodynamics)|thermodynamic work]] is less than that of the initial form. For example, [[Heat transfer|transfer of energy as heat]] is dissipative because it is a transfer of energy other than by thermodynamic work or by transfer of matter, and [[Entropy (energy dispersal)|spreads]] previously concentrated energy. Following the [[second law of thermodynamics]], in conduction and radiation from one body to another, the [[entropy]] varies with [[temperature]] (reduces the capacity of the combination of the two bodies to do work), but never decreases in an isolated system.

In [[mechanical engineering]], '''dissipation''' is the irreversible conversion of [[mechanical energy]] into [[thermal energy]] with an associated increase in entropy.<ref>{{Cite book |last=Escudier |first=Marcel |url=http://www.oxfordreference.com/view/10.1093/acref/9780198832102.001.0001/acref-9780198832102 |title=A Dictionary of Mechanical Engineering |last2=Atkins |first2=Tony |date=2019 |publisher=Oxford University Press |isbn=978-0-19-883210-2 |edition=2 |language=en |doi=10.1093/acref/9780198832102.001.0001}}</ref>

Processes with defined local temperature [[entropy production|produce entropy]] at a certain rate. The entropy production rate times local temperature gives the dissipated [[Power (physics)|power]]. Important examples of irreversible processes are: [[heat flow]] through a [[thermal resistance]], [[fluid flow]] through a flow resistance, diffusion (mixing), [[chemical reaction]]s, and [[electric current]] flow through an [[Electrical resistance and conductance|electrical resistance]] ([[Joule heating]]).
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== 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]]''.

== Examples ==

=== In hydraulic engineering ===
Dissipation is the process of converting mechanical energy of downward-flowing water into thermal and acoustical energy. Various devices are designed in stream beds to reduce the kinetic energy of flowing waters to reduce their [[erosion|erosive potential]] on banks and [[stream bed|river bottoms]]. Very often, these devices look like small [[waterfall]]s or [[waterfall#Types|cascades]], where water flows vertically or over [[riprap]] to lose some of its [[kinetic energy]].

=== Irreversible processes ===
Important examples of irreversible processes are: 
# Heat flow through a thermal resistance
# Fluid flow through a flow resistance
# Diffusion (mixing)
# Chemical reactions<ref>Glansdorff, P., [[Ilya Prigogine|Prigogine, I.]] (1971). ''Thermodynamic Theory of Structure, Stability, and Fluctuations'', Wiley-Interscience, London, 1971, {{ISBN|0-471-30280-5}}, p. 61.</ref><ref>Eu, B.C. (1998). ''Nonequilibrium Thermodynamics: Ensemble Method'', Kluwer Academic Publications, Dordrecht, {{ISBN|0-7923-4980-6}}, p. 49,</ref>
# Electrical current flow through an electrical resistance ([[Joule heating]]).

=== Waves or oscillations ===
[[Wave]]s or [[oscillation]]s, lose [[energy]] over [[time]], typically from [[friction]] or [[turbulence]]. In many cases, the "lost" energy raises the [[temperature]] of the system. For example, a [[wave]] that loses [[amplitude]] is said to dissipate. The precise nature of the effects depends on the nature of the wave: an [[atmospheric wave]], for instance, may dissipate close to the surface due to [[friction]] with the land mass, and at higher levels due to [[radiative cooling]].

== History ==
{{See also |Timeline of thermodynamics}}
The concept of dissipation was introduced in the field of thermodynamics by [[William Thomson, 1st Baron Kelvin|William Thomson]] (Lord Kelvin) in 1852.<ref>W. Thomson ''On the universal tendency in nature to the dissipation of mechanical energy'' Philosophical Magazine, Ser. 4, p.&nbsp;304 (1852).</ref> Lord Kelvin deduced that a subset of the above-mentioned irreversible dissipative processes will occur unless a process is governed by a "perfect thermodynamic engine". The processes that Lord Kelvin identified were friction, diffusion, conduction of heat and the absorption of light.

==See also==
*[[Entropy production]]
**[[General equation of heat transfer]]
*[[Flood control]]
*[[Principle of maximum entropy]]
*[[Two-dimensional gas]]

==References==
{{Reflist}}
===General References===
* "Dissipative system, a system that loses energy in the course of its time evolution." {{Cite book| publisher = Springer-Verlag| isbn = 978-0-387-21632-4| last1 = Benenson| first1 = W.| last2 = Harris| first2 = J. W.| last3 = Stocker| first3 = H.| last4 = Lutz| first4 = H.| title = Handbook of Physics| location = New York, NY| date = 2002| chapter = 6.1.3| page = 219}}
{{Footer energy}}

[[Category:Thermodynamic processes]]
[[Category:Thermodynamic entropy]]
[[Category:Non-equilibrium thermodynamics]]
[[Category:Dynamical systems]]