A closed system is a natural

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. The environment is ignored except for its effects on the ...

that does not allow transfer of matter in or out of the system, although — in contexts such as 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 ...

, chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...

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 speciali ...

— the transfer of energy (''e.g.'' as work or heat) is allowed.
In physics

In classical mechanics

In nonrelativisticclassical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by class ...

, 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. The environment is ignored except for its effects on the ...

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 of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as ...

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 so far removed from other systems that it does not interact with them.
# a thermodynamic system enclosed by rigid immovable walls through which neither ...

in 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 th ...

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

Inthermodynamics
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 th ...

, a closed system can exchange energy (as heat
In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...

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
** Working animal, an animal ...

) 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 parti ...

, with its surroundings.
An isolated system
In physical science, an isolated system is either of the following:
# a physical system so far removed from other systems that it does not interact with them.
# a thermodynamic system enclosed by rigid immovable walls through which neither ...

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 substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaki ...

, 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:
:$\backslash sum\_^m\; a\_N\_j=b\_i$
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 concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In therm ...

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\backslash hbar\; \backslash frac\; \backslash Psi(\backslash mathbf,\; t)\; =\; \backslash hat\; \backslash Psi(\backslash mathbf,\; t) where is theimaginary unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and ...

, is the Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...

divided by , the symbol indicates a partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Pa ...

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

, (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-valued probability amplitude, and the probabilities for the possible results of measurements ...

of the quantum system, and is the Hamiltonian operator
Operator may refer to:
Mathematics
* A symbol indicating a mathematical operation
* Logical operator or logical connective in mathematical logic
* Operator (mathematics), mapping that acts on elements of a space to produce elements of another s ...

(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. reachingthermal 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 ...

).
In engineering

In anengineering
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 speciali ...

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 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 ...

* Isolated system
In physical science, an isolated system is either of the following:
# a physical system so far removed from other systems that it does not interact with them.
# a thermodynamic system enclosed by rigid immovable walls through which neither ...

* Open system (systems theory)
* Sense and Respond
* Thermodynamic system
A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that a ...

References

{{Reflist Cybernetics Systems theory Thermodynamic systems