Exponential relaxation time ($u(t)-u_{\infty }=[u(0)-u_{\infty }]e^{-t/\tau }$)

For a stable first-order linear equation $u^{\prime }=-(u-u_{\infty })/\tau$, the time $\tau >0$ is the interval over which a deviation from equilibrium decays by the factor $e^{-1}$. This is the dynamical exponential-decay sense, distinct from a Markov chain's spectral relaxation time.