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What is entropy?

Entropy is a state function of a system, it depends only on the equilibrium state of the system. The chenge in entropy between initial and final equilibrium states is
$\Delta S=\int_{i}^{f}\frac{dQ}{T}$
where dQ is the infinitesimal heat transfer that takes place reversibly. The change in entropy for process, including irreversible one between given initial and final equilibrium state, is the same.The second law of thermodynamics may be expressed in terms of entropy, $\Delta S \geqslant 0$.
For reversible process  $\Delta S = 0$.
For irreversible process  $\Delta S > 0$.
Entropy is a measure of the disorder in a system. The second law states that the natural (irreversible) process tend to evolve to state of greater disorder, or from states of low probability to states of high probability.