Isolated system

Encyclopedia

In the natural sciences an

without any external exchange. If it has any surroundings, it does not interact

with them. It obeys in particular the first of the conservation law

s: its total energy - mass stays constant. Matter and energy cannot enter or exit, but can only move around inside.

An example is in the study of spacetime

, where it is assumed that asymptotically flat spacetime

s exist.

Truly isolated physical systems do not exist in reality (except perhaps for the universe as a whole), because, for example, there is always gravity between a system with mass, and masses elsewhere. However, real systems may behave nearly as an isolated system for finite (possibly very long) times. The concept of an isolated system can serve as a useful model approximating many real-world situations. It is an acceptable idealization

used in constructing mathematical model

s of certain natural phenomena

; e.g., the Sun

and planet

s in our solar system

, and the proton

and electron

in a hydrogen atom

are often treated as isolated systems. But from time to time, a hydrogen atom will interact with electromagnetic radiation

and go to an excited state

.

In the attempt to justify the postulate of entropy

increase in the second law of thermodynamics

, Boltzmann’s H-theorem

used equations which assumed a system (for example, a gas

) was isolated. That is all the mechanical degrees of freedom could be specified, treating the walls simply as mirror

boundary conditions. This inevitably led to Loschmidt's paradox

. However, if the stochastic

behavior of the molecule

s in actual walls is considered, along with the randomizing effect of the ambient, background thermal radiation

, Boltzmann’s assumption of molecular chaos

can be justified.

It is important to note that isolated systems are not equivalent to closed systems. Closed systems cannot exchange matter with the surroundings, but can exchange energy. Isolated systems can exchange neither matter nor energy with their surroundings, and as such are only theoretical. (The universe as a whole might be considered one.)

**isolated system**, as contrasted with an open system, is a physical systemPhysical system

In physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...

without any external exchange. If it has any surroundings, it does not interact

Interaction

Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect...

with them. It obeys in particular the first of the conservation law

Conservation law

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....

s: its total energy - mass stays constant. Matter and energy cannot enter or exit, but can only move around inside.

An example is in the study of spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

, where it is assumed that asymptotically flat spacetime

Asymptotically flat spacetime

An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime....

s exist.

Truly isolated physical systems do not exist in reality (except perhaps for the universe as a whole), because, for example, there is always gravity between a system with mass, and masses elsewhere. However, real systems may behave nearly as an isolated system for finite (possibly very long) times. The concept of an isolated system can serve as a useful model approximating many real-world situations. It is an acceptable idealization

Idealization

Idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false. Often these assumptions are used to make models easier to understand or solve. Many times idealizations do not harm the predictive accuracy of the model for one reason or...

used in constructing mathematical model

Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

s of certain natural phenomena

Phenomenon

A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'...

; e.g., the Sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

and planet

Planet

A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s in our solar system

Solar System

The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

, and the proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

and electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

in a hydrogen atom

Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force...

are often treated as isolated systems. But from time to time, a hydrogen atom will interact with electromagnetic radiation

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

and go to an excited state

Excited state

Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....

.

In the attempt to justify the postulate of entropy

Entropy

Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

increase in the second law of thermodynamics

Second law of thermodynamics

The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

, Boltzmann’s H-theorem

H-theorem

In Classical Statistical Mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process. H-theorem follows from considerations of Boltzmann's equation...

used equations which assumed a system (for example, a gas

Gas

Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

) was isolated. That is all the mechanical degrees of freedom could be specified, treating the walls simply as mirror

Mirror

A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

boundary conditions. This inevitably led to Loschmidt's paradox

Loschmidt's paradox

Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics...

. However, if the stochastic

Stochastic

Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

behavior of the molecule

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s in actual walls is considered, along with the randomizing effect of the ambient, background thermal radiation

Thermal radiation

Thermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation....

, Boltzmann’s assumption of molecular chaos

Molecular chaos

In kinetic theory in physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position...

can be justified.

It is important to note that isolated systems are not equivalent to closed systems. Closed systems cannot exchange matter with the surroundings, but can exchange energy. Isolated systems can exchange neither matter nor energy with their surroundings, and as such are only theoretical. (The universe as a whole might be considered one.)