Quasi-static process
A change carried out so slowly that the system passes through a continuous succession of equilibrium states — the condition for a process to have a path on a PV diagram.
Definition
A quasi-static process is one conducted slowly enough that the system remains arbitrarily close to thermodynamic equilibrium at every instant. Only then does it possess a single, well-defined pressure and temperature throughout, and only then can it be represented as a continuous curve on a pressure–volume diagram. Squeeze a gas suddenly and it bunches and swirls with no single pressure to plot; squeeze it slowly and each intermediate state is a genuine equilibrium.
Quasi-static is a necessary condition for reversibility but not a sufficient one: a process can be quasi-static yet still irreversible if friction or other dissipation is present. Reversibility requires quasi-static change plus the absence of all dissipative effects.
The idealisation matters because the analytic work formulas of thermodynamics — W = ∫P dV along an isotherm or adiabat — assume a definite pressure at each volume, which exists only for a quasi-static path. Real processes approximate it whenever they are slow compared with the system's relaxation time.
History
Implicit in Carnot's reversible engine and Clapeyron's smooth PV curves, the notion was sharpened in the later nineteenth century as thermodynamics distinguished the conditions for reversibility from the mere slowness of a process.