  We introduce a modification of Voiculescu's free entropy which coincides with
the liminf variant of Voiculescu's free entropy on extremal states, but is a
concave upper semi-continuous function on the trace state space. We also extend
the orbital free entropy of Hiai, Miyamoto and Ueda to non-hyperfinite
multivariables and prove freeness in case of additivity of Voiculescu's entropy
(or vanishing of our extended orbital entropy).
