A physical system is a system that is comprised of matter and energy. In this context a "system" is taken to mean "an interelated, interworking set of objects that operates autonomously".

For example, a lake is a physical system, and a written story about a lake is a conceptual system. In order for the conceptual system to operate, the physical system (human reader) has to "run" it but the physical system runs on its own.

The complexity of a physical system is equal to the probability of being in a particular state vector.

If one considers a classical newtonian ball situation with a number of perfectly moving physical bodies bouncing off the walls of a container, the probability of the system does not change. The entropy of the system changes over time, but the probability of the state vector does not change. One can consider the complexity of this system, and the complexity of this system 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 there are some low probability systems which are able to sustain themselves through time.

In mathematical systems, one can consider the complexity of particular states more easily. For example, if one considers a Turing machine which generates random symbols and then utilizes these symbols as an algorithm to create a new series of symbols the complexity of the final string of symbols is nearly mathematically equivalent to Algorithmic information theory- the minimum size of a string required to produce a larger string on a Turing machine.

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Conceptual vs Physical Systems