As far as I know, the definition of a reversible process is simply "a process that can be reversed". Meaning, that for an isolated global system containing the subsystem in question, its thermodynamic variables can hypothetically be restored to their initial values -after reaching their final values- without violating the postulates of Thermodynamics.
The definition of a reversible process is not "a process consisting of an almost infinite number of steps each of which has the global system in almost equilibrium", nor is it "a process where the net entropy change of the global system is zero".
Those two are proposed statements, and need to be proven equal to the definition by a theorem of some kind.
I ask if anyone could provide me with the deduction of those two statements from the postulates of Thermodynamics.
A few notes:
Please include very clearly what formulation of the postulates is being used. They can be wildly different.
For simplicity, I consider an isolated system (for which the first and second postulates apply), which may be subdivided into other sub systems.
I'm asking about classical thermodynamics, not statistical mechanics.
In a step of an idealized Quasi Static Process, some thermodynamic variables change by an infinitesimal amount. Yet they add over all of the steps to give a total non-infinitesimal change.
If the conventional definition of Reversible Process is actually one of the two statements, then the question remains the same, a proof of equivalence of the statements.