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An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

4 votes

Gibbs free energy and entropy

According to the Second Law, the entropy of an isolated system can never decrease. Hence, for a process to occur spontaneously in an isolated system, it must increase entropy. … For example, in the preceding example, the entropy of the water actually decreased. …
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Entropy of micro canonical ensemble

If you have one "die" (singular of the plural "dice") and all you care about is which face is up, then the number of microstates is the number of faces. For example, for a six-sided die, $\Omega=6$. I …
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Is Mechanical Equilibrium Really Driven by Entropy Increase?

The notion is this: When a system cannot increase its internal entropy, the Second Law of Thermodynamics (basically, that entropy increases until an equilibrium is reached) states that it will reach equilibrium … If the system can't increase its entropy, then its energy isn't doing it any good, at least as far as increasing the universe's entropy. …
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