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First I initially consider the work performed on the resistor and no heat is added.

TdS = dU - dW = 0, since the change in the energy is due solely to the work.

Then the resistor is brought into contact with the bath and heat flows from the resistor to the bath

TdS = -dW = -I^2*R*t.

So I'd get a negative change in entropy for the entire process (for the resistor). Where in teh cycle have I made a mistake?