Dark energy models in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>w</mml:mi><mml:mo>−</mml:mo><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>plane

We examine the behavior of dark energy models in the plane defined by $w$ (the equation of state parameter for the dark energy) and ${w}^{\ensuremath{'}}$ (the derivative of $w$ with respect to the logarithm of the scale factor). For nonphantom barotropic fluids with positive squared sound speed, we find that ${w}^{\ensuremath{'}}&lt;3w(w+1)$, the opposite of the bound on quintessence models previously derived by Caldwell and Linder. Thus, these barotropic models and quintessence models for the dark energy occupy disjoint regions in the $w\ensuremath{-}{w}^{\ensuremath{'}}$ plane. We also derive two new bounds for quintessence models in the $w\ensuremath{-}{w}^{\ensuremath{'}}$ plane: the first is a general bound for any scalar field with a monotonic potential, while the second improves on the Caldwell-Linder bound for tracker quintessence models. Observationally distinguishing barotropic models from quintessence models requires $\ensuremath{\sigma}({w}^{\ensuremath{'}})\ensuremath{\lesssim}1+w$.

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