  We introduce a continuum framework for the energetics of particle-size
segregation in bidisperse granular flows. Building on continuum segregation
equations and a recent segregation flux model, the proposed framework offers
general analytical expressions to study the physics of granular flows from a
mechanical energy perspective. To demonstrate the framework's applicability, we
examined the energetics in shear-driven flows. Numerical experiments with
varying frictional coefficients and particle-size ratios revealed two distinct
phases in the associated energetics with particle segregation and diffusive
remixing, and that the potential energy to the kinetic energy ratio in the
steady state follows the scaling relationship $\hat{E}^{(s)}_{gp} /
\hat{E}^{(s)}_{k} \propto Pe^{-1/2}_{sr}$ for $0.4 \leq Pe_{sr} \leq 300$, the
segregation-rheology P\'eclet number. Our findings hint that the bulk
segregation-mixing state can be predicted and controlled using $Pe_{sr}$,
determined from known system parameters, providing a impactful tool for
engineering and geophysical applications.
