In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be characterized by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp(-t/τ).

Let the homogenous differential equation:

model damped unforced oscillations of a weight on a spring.

The displacement will then be of the form Failed to parse (Missing texvc executable; please see math/README to configure.): y(t) = A e^{-t/T} \cos(\mu t - \delta) . The constant T is called the relaxation time of the system and the constant μ is the quasi-frequency.

In an RC circuit containing a charged capacitor and a resistor, the voltage decays exponentially:

The constant Failed to parse (Missing texvc executable; please see math/README to configure.): \tau = RC\

In condensed matter physics, relaxation is usually studied as a linear response to a small external perturbation. Since the underlying microscopic processes are active even in the absence of external perturbations, one can also study "relaxation in equilibrium" instead of the usual "relaxation into equilibrium" (see fluctuation-dissipation theorem).