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entropy en·tro·py (ěn'trə-pē)
For a closed thermodynamic system, a quantitative measure of the amount of thermal energy not available to do work.
A measure of the disorder or randomness in a closed system.
A measure of the amount of energy in a physical system not available to do work. As a physical system becomes more disordered, and its energy becomes more evenly distributed, that energy becomes less able to do work. For example, a car rolling along a road has kinetic energy that could do work (by carrying or colliding with something, for example); as friction slows it down and its energy is distributed to its surroundings as heat, it loses this ability. The amount of entropy is often thought of as the amount of disorder in a system. See also heat death.
A measure of the disorder of any system, or of the unavailability of its heat energy for work. One way of stating the second law of thermodynamics — the principle that heat will not flow from a cold to a hot object spontaneously — is to say that the entropy of an isolated system can, at best, remain the same and will increase for most systems. Thus, the overall disorder of an isolated system must increase.
Note: Entropy is often used loosely to refer to the breakdown or disorganization of any system: “The committee meeting did nothing but increase the entropy.”
Note: In the nineteenth century, a popular scientific notion suggested that entropy was gradually increasing, and therefore the universe was running down and eventually all motion would cease. When people realized that this would not happen for billions of years, if it happened at all, concern about this notion generally disappeared.
A measure of the disorder of a system. Systems tend to go from a state of order (low entropy) to a state of maximum disorder (high entropy).
The entropy of a system is related to the amount of information it contains. A highly ordered system can be described using fewer bits of information than a disordered one. For example, a string containing one million "0"s can be described using run-length encoding as [("0", 1000000)] whereas a string of random symbols (e.g. bits, or characters) will be much harder, if not impossible, to compress in this way.
Shannon's formula gives the entropy H(M) of a message M in bits:
H(M) = -log2 p(M)
Where p(M) is the probability of message M.