  The normal-conducting state of the superconductor UTe$_2$ is studied by
entropy analysis for magnetic fields along the $b$-axis, obtained from
magnetization using the relation $(\partial M/\partial T)_B=(\partial
S/\partial B)_T$. We observe a strong increase in entropy with magnetic field
due to metamagnetic fluctuations (spatially uniform, $Q=0$). The field
dependence is well described by the Hertz-Millis-Moriya theory for quantum
criticality of itinerant metamagnetism. Notably, the lower bound of the
quantum-critical region coincides well with the position of the minimum in the
superconducting transition temperature $T_c(B)$. Hence, our results suggest
that $Q=0$ fluctuations reinforce the superconductivity.
