  We consider open quantum systems with dynamics described by master equations
that have perturbative expansions in the system-environment interaction. We
show that, contrary to intuition, full-time solutions of order-2n accuracy
require an order-(2n+2) master equation. We give two examples of such
inaccuracies in the solutions to an order-2n master equation: order-2n
inaccuracies in the steady state of the system and order-2n positivity
violations, and we show how these arise in a specific example for which exact
solutions are available. This result has a wide-ranging impact on the validity
of coupling (or friction) sensitive results derived from second-order
convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
