  The temperature dependence of the integrated optical conductivity I(T)
reflects the changes of the kinetic energy as spin and charge correlations
develop. It provides a unique way to explore experimentally the kinetic
properties of strongly correlated systems. We calculated I(T) in the frame of a
t-J-V model at quarter-filling for ladder systems, like NaV_2O_5, and show that
the measured strong T dependence of I(T) for NaV_2O_5 can be explained by the
destruction of short range antiferromagnetic correlations. Thus I(T) provides
detailed information about super-exchange and magnetic energy scales.
