Significance of Reversibility in Thermodynamics

Reversibility (Section 4.7.3.1) is central to the Carnot cycle's theoretical importance, so it is worth restating precisely why. A reversible process is genuinely bidirectional: run forward or run backward, it follows exactly the same sequence of states either way. This can only happen if the process proceeds in infinitesimally small steps, with the difference between any two successive, infinitesimally-close states being vanishingly small — which in turn is only possible if the system remains in thermodynamic equilibrium (Section 4.6.1) with its environment at every single instant throughout the change.

An irreversible process, in sharp contrast, is inherently unidirectional: it can only proceed in one direction, and — crucially — a system undergoing an irreversible process is, at some point along the way, NOT in thermal equilibrium with its environment (this is exactly what makes the process irreversible in the first place, per Section 4.7.3.1). …