TL;DR
This paper revisits the concept of orbital free entropy, providing a new definition that removes the hyperfiniteness assumption and aligns closely with the original formulation.
Contribution
It introduces a new definition of orbital free entropy that does not require hyperfiniteness, improving the theoretical framework.
Findings
New definition aligns with the original orbital free entropy
Eliminates the need for hyperfiniteness assumption
Connects with recent generalizations by Biane and Dabrowski
Abstract
We give another definition of orbital free entropy introduced by Hiai, Miyamoto and us, which does not need the hyperfiniteness assumption for each given random multi-variable. The present definition is somehow related to one of its several recent `generalizations' due to Biane and Dabrowski, but completely agrees with the original definition and much closer to the original approach.
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