In thermodynamics, entropy is formally defined as the change in a state variable S given by heat added to a system divided by the absolute temperature at which it is added, but this definition only yields a valid state variable (path-independent, zero net change over a closed cycle) when the heat transfer occurs reversibly. Reversibility requires a process to be both quasistatic (always infinitesimally close to equilibrium) and frictionless (no dissipative generation of heat); the Carnot cycle satisfies both conditions, which is why it can be used to prove entropy's validity as a state variable and why it represents the theoretical maximum-efficiency heat engine. For irreversible processes, applying Q/T directly does not return to zero over a closed cycle because friction generates additional heat, so entropy change for an irreversible path must instead be computed by substituting an equivalent reversible path between the same initial and final states.
In thermodynamics, entropy is formally defined as the change in a state variable S given by heat added to a system divided by the absolute temperature at which it is added, but this definition only y…