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A closed system is a
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The environment is ignored except f ...
that does not allow transfer of matter in or out of the system, though, in different contexts, such as
physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

,
chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during a with other . ...

or
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...

, the transfer of energy is or is not allowed.

In physics

In classical mechanics

In
nonrelativistic The theory of relativity usually encompasses two interrelated theories by Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest ph ...
classical mechanics, a closed system is a
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The environment is ignored except f ...
that doesn't exchange any matter with its surroundings, and isn't subject to any net
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

whose source is external to the system. A closed system in classical mechanics would be equivalent to an
isolated system In physical science, an isolated system is either of the following: # a physical system In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , i ...
in
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

. Closed systems are often used to limit the factors that can affect the results of specific problem or experiment.

In thermodynamics

In
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

, a closed system can exchange energy (as
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

or
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
) but not
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particl ...
, with its surroundings. An
isolated system In physical science, an isolated system is either of the following: # a physical system In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , i ...
cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter. (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.) For a simple system, with only one type of particle (atom or molecule), a closed system amounts to a constant number of particles. However, for systems which are undergoing a
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...
, there may be all sorts of molecules being generated and destroyed by the reaction process. In this case, the fact that the system is closed is expressed by stating that the total number of each elemental atom is conserved, no matter what kind of molecule it may be a part of. Mathematically: :$\sum_^m a_N_j=b_i$ where $N_j$ is the number of j-type molecules, $a_$ is the number of atoms of element $i$ in molecule $j$ and $b_i$ is the total number of atoms of element $i$ 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 Thermodynamic equilibrium is an axiomatic An axiom, postulate or assumption is a statement that is taken to be true True most commonly refers to truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online ...
is required to simplify the situation.

In quantum physics

This equation, called 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). $i\hbar \frac \Psi(\mathbf, t) = \hat \Psi(\mathbf, t)$ where is the
imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation In algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad area ...
, is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
divided by , the symbol indicates a
partial derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

with respect to
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

, (the Greek letter psi) is the
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex number, complex-valued probability amplitude, and the probabilities for the possible results of ...

of the quantum system, and is the Hamiltonian operator (which characterizes the total energy of any given wave function and takes different forms depending on the situation).

In chemistry

In chemistry, a closed system is where no reactants or products can escape, only heat can be exchanged freely (e.g. an ice cooler). A closed system can be used when conducting chemical experiments where temperature is not a factor (i.e. reaching
thermal equilibrium Two physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The enviro ...

).

In engineering

In an
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...

context, a closed system is a bound system, i.e. defined, in which every input is known and every resultant is known (or can be known) within a specific time.

See also

* Glossary of systems theory *
Dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in a Manifold, geometrical space. Examples include the mathematical models that describe the ...
*
Isolated system In physical science, an isolated system is either of the following: # a physical system In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , i ...
*
Open system (systems theory) An open system is a system that has external interactions. Such interactions can take the form of information, energy, or material transfers into or out of the system boundary, depending on the discipline which defines the concept. An open system ...
* Sense and Respond *
Thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, whic ...

References

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Cybernetics Cybernetics is a Transdisciplinarity, transdisciplinary approach for exploring regulatory systems with feedback, their structures, constraints, and possibilities. Cybernetics is relevant to the study of systems, such as mechanical, physical, biol ...
Systems theory Thermodynamic systems