@article{oai:nagoya.repo.nii.ac.jp:00028434, author = {HIAI, FUMIO and MIYAMOTO, TAKUHO and UEDA, YOSHIMICHI}, issue = {02}, journal = {International Journal of Mathematics}, month = {}, note = {Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy χorb for non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties, the relation of χorb with the usual free entropy χ is shown. Moreover, the dimension counterpart δ0,orb of χorb is discussed, and we obtain the relation between δ0,orb and the original free entropy dimension δ0 together with applications to δ0 itself.}, pages = {227--273}, title = {ORBITAL APPROACH TO MICROSTATE FREE ENTROPY}, volume = {20}, year = {2009} }