  We investigate the scaling behaviors of bipartite fluctuations $\mathcal{F}$
of conserved quantities across a class of interaction-driven quantum phase
transitions out of Landau fermi liquids, where other phases involve
fermi-surface states of fractionalized degrees of freedom. Examples of such
phases include (compressible) composite fermi liquids for spinless electrons
and (incompressible) spin-liquid Mott insulators for spin-$1/2$ electrons. The
two sides of the critical points are typically distinguished by distinct
leading-order scalings of bipartite charge fluctuations, $\mathcal{F}\sim L\log
(L)$ in Landau fermi liquids, and $\mathcal{F}\sim L$ in the other phases,
where $L$ is the linear size of the subsystem under bipartition. In the case of
composite fermi liquids (with continuous translational and rotational
invariance), we also identify a universal constant term
$-\mathtt{F}(\theta)\sigma_{xy}/\pi$ arising when the subsystem geometry
incorporates a sharp corner. Here, $\mathtt{F}(\theta)$ represents a function
of the corner angle, and $\sigma_{xy}$ denotes the Hall conductivity. At the
critical point of each example, we find that the leading-order scaling
$\mathcal{F}\sim L$ is accompanied by a subleading universal corner
contribution $-\mathtt{F}(\theta)C_{\rho}\log(L)$ with the same angle
dependence $\mathtt{F}(\theta)$. The universal coefficient $C_{\rho}$ is linked
to the predicted universal longitudinal (and Hall) resistivity jump
$\Delta\rho_{xx}$ (and $\Delta\rho_{xy}$) at the critical point.
