Home » Thermodynamics

Reversible process

An idealized process that can be reversed leaving no net change in the system and surroundings, implying zero entropy production.

Reversible process

A reversible process is a thermodynamic process that can be reversed by an infinitesimal change in external conditions so that both the system and the surroundings are restored exactly to their initial states. Operationally, a reversible process proceeds through a continuous family of equilibrium states and contains no dissipative effects (no friction, viscosity, finite-temperature-difference heat flow, diffusion, etc.).

Every reversible process is quasistatic , but the converse need not hold.

Physical interpretation

Reversibility is a limiting idealization: the system is always (and everywhere) arbitrarily close to equilibrium , and the driving “forces” are infinitesimal. Intuitively, a reversible process is one that can be run backward without leaving “footprints” in the environment—no wasted work and no net spreading of energy into unavailable forms.

Key entropy relation

The hallmark of reversibility is zero entropy production. For a reversible transfer of heat with the system at temperature $T$ , the change in the thermodynamic entropy $S$ satisfies the Clausius equality:

dS = \frac{\delta Q_{\mathrm{rev}}}{T}.

Between two equilibrium states $A \to B$ along a reversible path,

\Delta S = \int_{A}^{B} \frac{\delta Q_{\mathrm{rev}}}{T}.

This is the equality case of the Clausius inequality , a core consequence of the second law .

For a reversible cycle , the system returns to its initial state, and the entropy balance implies

\oint \frac{\delta Q_{\mathrm{rev}}}{T} = 0.

Extremal work principle (common thermodynamic use)

Under fixed reservoir constraints, reversible processes are the benchmark for “best possible” performance: they deliver maximum work output (or require minimum work input) compared with any irreversible alternative connecting the same equilibrium endpoints.

This benchmark is often expressed using free energies. For example, in an isothermal setting (fixed $T$ ) the maximum useful work is tied to the decrease of the Helmholtz free energy ; at fixed $T$ and $P$ , it is tied to the decrease of the Gibbs free energy , with the notion of “useful” excluding boundary $P\,dV$ work as specified by the $P\,dV$ convention .