Classical thermodynamics always discusses entropy in the light of reversible processes, and it lies at the heart of the definition of entropy. But do these reversible processes exist in Nature, or are they just a gedankenexperiment?
Since if they do not exist, then classical thermodynamics gives a lower bound on the increase of entropy, but says nothing about the difference in entropy between the reversible and irreversible process. Doesn't this make the classical definition useless for a quantitative approach? Or is there proof that the entropy difference between the reversible and irreversible process is small for most everyday cases?