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I can explain part of your question. Basically work is being done in a reversible process but not for an irreversible process. When work is being done, q(surr) exists therefore entropy change of the surroundings does too. This will usually equal the entropy change of the system making total entropy change 0. In an irreversible process no work is done so q(surr) = 0 therefore change in S of surroundings is 0 as well. This means delta S system equals delta S total.
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