  Using first-principles molecular dynamics, we calculated the equation of
state and shock Hugoniot of various boron phases. We find a large mismatch
between Hugoniots based on existing knowledge of the equilibrium phase diagram
and those measured by shock experiments, which could be reconciled if the
$\alpha$-B$_{12}$/$\beta \rightarrow\gamma$-B$_{28}$ transition is
significantly over-pressurized in boron under shock compression. Our results
also indicate that there exists an anomaly and negative Clapeyron slope along
the melting curve of boron at 100 GPa and 1500--3000 Kelvin. These results
enable in-depth understanding of matter under shock compression, in particular
the significance of compression-rate dependence of phase transitions and
kinetic effects in experimental measurements.
