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{{shortShort description|Does not allow certain typesType of transfers (such as transfer of matter) in or out of the system}}
{{About|closed [[physical system]]s as the term is used in the physical sciences concept|software (inthe computing) whose source code is kept secretconcept|Closed source software}}
 
A '''closed system''' is a natural [[physical system]] that does not allow transfer of [[matter]] in or out of the system, though, although{{snd}}in differentthe contexts, such asof [[physics]], [[chemistry]] or, [[engineering]], etc.{{snd}}the transfer of energy is(e.g. as work or isheat) notis allowed.
 
==In physicsPhysics==
 
===In classical mechanics===
In [[Theory of relativity|nonrelativistic]] [[classical mechanics]], a closed system is a [[physical system]] that doesn'tdoes not exchange any matter with its surroundings, and isn'tis not subject to any net [[force]] whose source is external to the system.<ref>{{cite book|last=Rana|first=N.C.|author2=P.S. Joag|title=Classical Mechanics|date=1991|page=78|isbn=978-0-07-460315-4}}</ref><ref>{{cite book|last=Landau|first=L.D.|author-link=Lev Landau|author2=E.M. Lifshitz|title=Mechanics|edition=third|date=1976|page=8|isbn=978-0-7506-2896-9}}</ref> A closed system in classical mechanics would be equivalent to an [[isolated system]] in [[thermodynamics]]. Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment.
 
===In thermodynamics===
{{main article|Thermodynamic system}}
[[File:Diagram Systems.pngsvg|thumb|Properties of Isolatedisolated, closed, and open systems in exchanging energy and matter.]]
 
In [[thermodynamics]], a closed system can exchange energy (as [[heat]] or [[mechanical work|work]]) but not [[matter]], with its surroundings.
An [[isolated system]] cannot exchange any heat, work, or matter with the surroundings, while an [[Thermodynamic system#Open system|open system]] can exchange energy and matter.<ref>[[Ilya Prigogine|Prigogine, I.]], Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London, p. 66.</ref><ref>[[László Tisza|Tisza, L.]] (1966). ''Generalized Thermodynamics'', M.I.T Press, Cambridge MA, pp. 112–113.</ref><ref>[[Edward A. Guggenheim|Guggenheim, E.A.]] (1949/1967). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', (1st edition 1949) 5th edition 1967, North-Holland, Amsterdam, p. 14.</ref><ref>Münster, A. (1970). ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, pp. 6–7.</ref><ref>Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of ''Thermodynamics'', pages 1–97 of volume 1, ed. W. Jost, of ''Physical Chemistry. An Advanced Treatise'', ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081, p. 3.</ref><ref>Tschoegl, N.W. (2000). ''Fundamentals of Equilibrium and Steady-State Thermodynamics'', Elsevier, Amsterdam, {{ISBN|0-444-50426-5}}, p. 5.</ref><ref>Silbey, R.J., [[Robert A. Alberty|Alberty, R.A.]], Bawendi, M.G. (1955/2005). ''Physical Chemistry'', fourth edition, Wiley, Hoboken NJ, p. 4.</ref> (This scheme of definition of terms is not uniformly used, though it is convenient for some purposes. In particular, some writers use 'closed system' where 'isolated system' is used here.<ref>[[Herbert Callen|Callen, H.B.]] (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, {{ISBN|0-471-86256-8}}, p. 17.</ref><ref>[[Dirk ter Haar|ter Haar, D.]], [[Harald Wergeland|Wergeland, H.]] (1966). ''Elements of Thermodynamics'', Addison-Wesley Publishing, Reading MA, p. 43.</ref>)
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:<math>\sum_{j=1}^m a_{ij}N_j=b_i</math>
 
where <math>N_j</math> is the number of j-type molecules, <math>a_{ij}</math> is the number of atoms of element ''<math>i''</math> in molecule ''<math>j''</math> and ''b<submath>ib_i</submath>'' is the total number of atoms of element ''<math>i''</math> in the system, which remains constant, since the system is closed. There will be one such equation for each different element in the system.
 
In thermodynamics, a closed system is important for solving complicated thermodynamic problems. It allows the elimination of some external factors that could alter the results of the experiment or problem thus simplifying it. A closed system can also be used in situations where [[thermodynamic equilibrium]] is required to simplify the situation.
 
===In quantum physics===
{{further|Quantum field theory}}This equation, called [[Schrödinger equation|Schrödinger's equation]], describes the behavior of an isolated or closed quantum system, that is, by definition, a system which does not interchange information (i.e. energy and/or matter) with another system. So if an isolated system is in some pure state |ψ(t) ∈ H at time t, where H denotes the Hilbert space of the system, the time evolution of this state (between two consecutive measurements).<ref>{{Cite book |last=Rivas |first=Ángel |title=Open Quantum Systems |lastlast2=RivasHuelga |firstfirst2=ÁngelSusana F. |last2author-link2=Susana F. Huelga|first2=Susana |date=October 2011 |publisher=Springer-Verlag |isbn=978-3-642-23354-8 |location=Berlin Heidelberg}}</ref>
 
:<math display="block">i\hbar \frac{\partial}{\partial t} \Psi\left(\mathbf{r}, t\right) = \hat{H} \Psi\left(\mathbf{r}, t\right) \,\!</math>
 
where {{math|''i''}} is the [[imaginary unit]], {{math|''ħ''}} is the [[Planck constant]] divided by {{math|2π}}, the symbol {{math|{{sfrac|∂|∂''t''}}}} indicates a [[partial derivative]] with respect to [[time]] {{math|''t''}}, {{math|''Ψ''}} (the Greek letter [[Psi (letter)|psi]]) is the [[wave function]] of the quantum system, and {{math|''Ĥ''}} is the [[Hamiltonian (quantum mechanics)|Hamiltonian]] [[Operator (physics)|operator]] (which characterizes the total energy of any given wave function and takes different forms depending on the situation).
 
==In chemistry==
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