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

Let the homogeneous differential equation:

model damped unforced oscillations of a weight on a spring.

The displacement will then be of the form ${\displaystyle y(t)=Ae^{-t/T}\cos(\mu t-\delta )}$. The constant T (${\displaystyle =2m/\gamma }$) 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 ${\displaystyle \tau =RC\ }$ is called the relaxation time or RC time constant of the circuit. A nonlinear oscillator circuit which generates a repeating waveform by the repetitive discharge of a capacitor through a resistance is called a relaxation oscillator.

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).

In continuum mechanics, stress relaxation is the gradual disappearance of stresses from a viscoelastic medium after it has been deformed.