Is there an irreversible process, where the entropy of the isolated system does not change?
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2nd principle says that for a given system $dS = \delta S_e + \delta S_c$. Therefore if $dS = 0$ it is still possible to have $\delta S_c > 0$ (i.e. an irrevesible transformation) if $S_e = \frac{Q}{T_{ext}} < 0$.
For example, the Joule-Thompson expansion is an isentropic transformation though irreversible.
What is always positive when we think about entropy is the entropy created $S_c$, not the difference of total enthalpy of your system, which can exchange entropy with other systems (if not a closed system).
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