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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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Definition of entropy
The variation of entropy only depends upon the initial and the final
state, and thus has the same value regardless if the transformation
was reversible or not.
[...] … $$\Delta S = \int_R \frac{\delta Q}{T}$$ $$\Delta S > \int_I
\frac{\delta Q}{T}$$
I understood that the RHS in the second equation is just an integral and does not represent the variation of entropy …