 It is nowadays a rather familiar fact that dynamical systems quite generally give rise to behavior of a statistical character, with the statistics given by the (or a) stationary probability distribution for the dynamics. So it is with Bohmian mechanics, except that for the Bohmian system stationarity is not quite the right concept. Rather it is the notion of equivariance that is relevant. A probability distribution on configuration space \(\varrho^{\psi}\), depending upon the wave function \(\psi\), is equivariant if   \[(\varrho^{\psi})_t = \varrho^{\psi_t}\]  where the dependence on \(t\) on the right arises from Schrödinger’s equation and on the left from the evolution on probability distributions arising from the flow that  the guiding equation  induces. Thus equivariance expresses the mutual compatibility, relative to \(\varrho^{\psi}\), of the Schrödinger evolution of the wave function and the Bohmian motion of the configuration. It is an immediate consequence of  the guiding equation  and the quantum continuity equation that \(\varrho^{\psi} = \lvert\psi(q)\rvert^2\) is equivariant. (It can be shown in fact that this is more or less the only equivariant possibility that is suitably local (Goldstein &amp; Struyve 2007).)