Evolutionary theory has long benefited from analogies with statistical physics—the other field of science dealing with large, evolving populations—, see e.g. \cite{Sella_2005,Mustonen_2010,de_Vladar_2011,Smerlak_2017}. More recently, Leuthäusser \cite{Leuth_usser_1986} and others \cite{Baake_1997,Saakian_2004} have highlighted a parallel between evolutionary models in genotype space and certain quantum spin systems, which can be leveraged to compute the quasispecies distribution \(Q\) for some special fitness landscapes \cite{BAAKE_2001}. But the scope of the analogy between evolution and non-equilibrium physics is, in fact, much broader: the interplay between selection and mutation is typical of localization phenomena in disordered systems \cite{Stollmann_2001}, be them classical or quantum. The linearized Crow-Kimura equation \ref{PAM}, for instance, is formally identical to the parabolic Anderson model  \cite{Zel_dovich_1987,Carmona_1994,K_nig_2016}, a simple model of intermittency in random fluid flows; the linearized Eigen model in turn resembles the Bouchaud trap model \cite{Bouchaud_1992}, a classical model of slow dynamics and ageing in glassy systems. These physical phenomena have obvious evolutionary counterparts: the Anderson localization transition corresponds to the error threshold; intermittency to epochal or punctuated evolution; tunnelling instantons to fitness valley crossings; and ageing to diminishing-return epistasis. The generalization of Nelson's mapping of the Scrödinger equation to a diffusion process presented in this paper implies that all are in fact unified under the familiar umbrella of Markovian metastability.