  Based on a generalized local Kolmogorov-Hill equation expressing the
evolution of kinetic energy integrated over spheres of size $\ell$ in the
inertial range of fluid turbulence, we examine a possible definition of entropy
and entropy generation for turbulence. Its measurement from direct numerical
simulations in isotropic turbulence leads to confirmation of the validity of
the fluctuation relation (FR) from non-equilibrium thermodynamics in the
inertial range of turbulent flows. Specifically, the ratio of probability
densities of forward and inverse cascade at scale $\ell$ is shown to follow
exponential behavior with the entropy generation rate if the latter is defined
by including an appropriately defined notion of ``temperature of turbulence''
proportional to the kinetic energy at scale $\ell$.
