  Recently, a class of gravitational backgrounds in 3+1 dimensions have been
proposed as holographic duals to a Lifshitz theory describing critical
phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our
earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of
the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that
the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where
$\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the
entropy density. This matches the expected behavior for a 2+1 dimensional
theory with a scaling symmetry $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to
\lambda^z t$.
