  We study fluctuations of the local energy cascade rate $\Phi_\ell$ in
turbulent flows at scales ($\ell$) in the inertial range. According to the
Kolmogorov refined similarity hypothesis (KRSH), relevant statistical
properties of $\Phi_\ell$ should depend on $\epsilon_\ell$, the viscous
dissipation rate locally averaged over a sphere of size $\ell$, rather than on
the global average dissipation. However, the validity of KRSH applied to
$\Phi_\ell$ has not yet been tested from data. Conditional averages such as
$\langle \Phi_\ell|\epsilon_{\ell}\rangle$ as well as of higher-order moments
are measured from Direct Numerical Simulations data, and results clearly adhere
to the predictions from KRSH. Remarkably, the same is true when considering
forward ($\Phi_\ell>0$) and inverse ($\Phi_\ell<0$) cascade events separately.
Measured ratios of forward and inverse cascade probability densities further
show that a fluctuation relation adhering to the KRSH can be observed, raising
the hope that important features of turbulence may be described using concepts
from non-equilibrium thermodynamics.
