Complexity of the universe
Relationship of complexity to entropy
Entropy, as we use it here, refers to the amount of energy available for doing work. The amount of usable energy in our universe is always going down. This is also known as the second law of thermodynamics.
Unfortunately, the word "entropy" was also used in information theory in
relation to Shannon's definition of information. Shannon's definition of information has nothing to do with the entropy of the universe as a whole except there are some similarities of math. The choice of the word entropy was a poor and confusing choice.
The second law of thermodynamics has many every day effects:
A hot cup of cocoa will get colder as the heat flows from the hot liquid to the cooler external room.
Resistors convert current into heat.
The flow of usable energy is relevant to complex systems because living organisms require usable energy to function.
Probability, as used in thermodynamics, means the probability that some specific change of usable energy will occur. It is expected that most systems will degrade towards less usable energy as time goes by.
Thermodynamics deals with the nature of heat and its conversion into other forms of energy. The greater the entropy of a system
the less available the energy is for doing useful work.
Does an increasing entropy necessarily mean a decreasing complexity?
No. A completely deterministic universe, such as a room of moving balls where they all start in one corner, would not change in complexity as time passed. The balls would scatter throughout the room. The entropy of this room would increase as time passed.
Note that the entropy changes in a probabilistic way because the useful energy of the balls is measured by partitioning the system and then saying, "What is the probability that we have X many balls in this partition?"
However, the future of this simple system is completely deterministic, and does not change in complexity. A completely deterministic system does not change in complexity.
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