  We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$
model and calculate the energy dissipation rate $W(\omega)$ that results due to
periodic modulation of random quadratic matrix elements with a frequency
$\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the
polaron energy splitting $\omega_R$ found recently (PRL 125, 196602),
demonstrating the physical significance of this energy scale. Next, we study
the effect of energy pumping with a finite amplitude at the resonance frequency
$\omega_R$ and calculate, in presence of this pumping, non-equilibrium
dissipation rate due to low-frequency parametric modulation. We found an
unusual phenomenon similar to "dry friction" in presence of pumping.
