Quantum equilibrium
= Quantum equilibrium
{title2=$\rho=|\Psi|^2$}
The ensemble density of actual configurations equals the squared norm of the guiding <wave function>. For spinless particles with $v_k=j_k/|\Psi|^2$, the Schrödinger <continuity equation> is $\partial_t|\Psi|^2+\sum_k\nabla_k\cdot(|\Psi|^2v_k)=0$. A density transported by the same guiding field satisfies the same equation, so initial equality is preserved. This equivariance is a consistency property, not a proof that every possible initial ensemble is in equilibrium. The physical account of the equilibrium assumption and subsystem statistics requires an additional argument.