Relaxationszeit

Relaxationszeit, or relaxation time, is the characteristic time constant that describes how quickly a physical system returns to equilibrium after a disturbance. In many processes the relaxation follows an exponential decay of the form ΔX(t) = ΔX(0) exp(-t/τ), so that τ represents the time needed for the deviation to drop by a factor of e. The specific value of τ depends on the underlying dynamics and the mechanism driving the return to equilibrium.

In electrical, mechanical and thermodynamic contexts, τ appears in a range of models. For a simple RC circuit, the voltage on a capacitor relaxes with τ = RC. In damped mechanical systems or first-order chemical kinetics, the approach to equilibrium also follows a characteristic time determined by the system's damping or reaction rates. In general, the relaxation time is related to the inverse of a rate or to a spectral property of the dynamics, such as the smallest nonzero eigenvalue of a transition operator or the correlation time of fluctuations.

In physics and chemistry, several specific relaxation times are common. In NMR and MRI, spin-lattice relaxation time T1 and spin-spin relaxation time T2 describe how magnetization returns to equilibrium after excitation, each reflecting different microscopic processes. In dielectrics, dielectric relaxation times describe how dipoles reorient in response to an alternating field, often modeled by Debye-type behavior. In complex materials and glasses, relaxation times can be broad and temperature-dependent, leading to slowed dynamics and observable aging effects.

Measurement typically involves perturbing the system and recording the time-dependent response, then fitting an exponential or stretched-exponential function to extract τ.