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In physics, a physical system is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which is ignored except for its effects on the system.
In a system that has moving physical bodies bouncing off the walls of a container, the system state probability is constant. The system's entropy increases, but the probability of the state vector does not change. The complexity of this system can be evaluated periodically, but it does not change.
In a physical system, a lower probability state vector is equivalent to a higher complexity. A self-sustaining low probability state vector allows the physical system to remain in a higher complexity state. The study of such systems as applied to our universe is in its infancy and speculative in nature, but it appears that some low probability systems are able to sustain themselves.
In mathematical systems, the complexity of particular states can be considered more easily. For example, a Turing machine generates random symbols then uses them to create a new sequences of symbols and the complexity of the final string of symbols is nearly mathematically equivalent to the minimum size of a string required to produce a larger string on a Turing machine as defined by algorithmic information theory.
The split between system and environment is the analyst's choice, generally made to simplify the analysis. An isolated system is one which has negligible interaction with its environment.
Often a system in this sense is chosen to correspond to the more usual meaning of system, such as a particular machine. For example, the water in a lake, the water in the left half of a lake or an individual atom of water in the lake can each be considered a physical system. In the study of quantum decoherence the "system" may refer to the macroscopic properties of an object (e.g. the position of a pendulum bob), while the relevant "environment" may be the internal degrees of freedom, described classically by the pendulum's thermal vibrations.
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