Generalized Langevin equation
= Generalized Langevin equation
{title2=$\dot V(t)=-\int_0^t\kappa(u)V(t-u)\,du+R(t)$}
A <Langevin equation> with a friction <memory kernel>, rather than only instantaneous friction. The equation couples the <velocity> to its earlier history through a causal <convolution>. Equilibrium noise and friction are related by a <generalized fluctuation-dissipation relation>. The name extends the <Langevin equation> associated with <Paul Langevin>.