= Exact spectral gap of normalized velocity relaxation
{title2=$\langle Lf,f\rangle=-\|(I-\Pi)f\|^2,\quad\|f_t-\Pi f_0\|=e^{-t}\|f_0-\Pi f_0\|$}
For the <normalized velocity-reset collision operator> on the weighted <Hilbert space>, $L=\Pi-I$ vanishes on the equilibrium direction and equals $-I$ on its <orthogonal complement>. The <spectral gap> is exactly one. Conservation of the projected component and the displayed energy identity give exact exponential decay of the remaining component; the full solution need not decay to zero.
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