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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 models of certain natural phenomena ; e.g., the planets in the Solar System , and the proton and electron in a hydrogen atom are often treated as isolated systems.
Overall, in an isolated system, the internal energy is constant and the entropy can never decrease. A closed system's entropy can decrease e.g. when heat is extracted from the system. Isolated systems are not equivalent to closed systems. Closed systems cannot exchange matter with the surroundings, but can exchange energy.
For a simple system, mechanical isolation is equivalent to a state of constant volume and any process which occurs in such a simple system is said to be isochoric. [1] The opposite of a mechanically isolated system is a mechanically open system, [citation needed] which allows the transfer of mechanical energy. For a simple system, a ...
The microcanonical ensemble represents an isolated system in which energy (E), volume (V) and the number of particles (N) are all constant. The canonical ensemble represents a closed system which can exchange energy (E) with its surroundings (usually a heat bath), but the volume (V) and the number of particles (N) are all constant.
In some systems the density of states is not monotonic in energy, and so T s can change sign multiple times as the energy is increased. [12] [13] The preferred solution to these problems is avoid use of the microcanonical ensemble. In many realistic cases a system is thermostatted to a heat bath so that the energy is not precisely known.
The Poincaré recurrence theorem considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the ...
The ideal isolated system, of which the entire universe is an example, is often only used as a model. Many systems in practical applications require the consideration of internal chemical or nuclear reactions, as well as transfers of matter into or out of the system.
In this context, "isolated" refers to the fact that the system has no (or at least negligible) interactions with the environment external to it. If the Hamiltonian of the system is denoted ^, then a complete set of basis states for the system is given in terms of the eigenstates of the Hamiltonian,