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A general rule for when they match is missing.","posed_since":"2013","precise":"For a quench $H_i \\to H_f$, the Loschmidt rate $l(t) = -\\operatorname{lim}_{N \\to \\infty} (1/N) \\operatorname{ln} \\mid\\langle\\psi_0\\mid \\operatorname{exp}(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$ can be nonanalytic at critical times $t_c$. Determine conditions on $(H_i, H_f)$ under which (a) such $t_c$ exist if and only if the quench crosses an equilibrium critical point and (b) $t_c$ coincide with zeros or sign changes of the order parameter. Answer: a classification valid beyond free-fermion models.","problem_ref":null,"references":"","settled_by":"A general criterion proved or verified across interacting nonintegrable models in $d = 1 \\text{ and } 2$.","status_note":"Counterexamples in both directions are known since 2014; no general criterion exists.","title":"When dynamical transitions coincide with equilibrium criticality or 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