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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.
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Does a closed system with fixed entropy imply an isolated system?
A closed system with fixed entropy does not imply an isolated system.
Fixed entropy means that $dS = 0$, the entropy of the system does not change. … If $dS=0$ then $\delta Q = 0$ and the above simplifies to
$$ dU = -\delta W \ .$$
So for a closed system at fixed entropy the change in energy goes as the work done in a reversible process. …