Free entropy χ: the microstates approach via large deviations

Abstract

An important concept in classical probability theory is Shannon’s notion of entropy. Having developed the analogy between free and classical probability theory, one hopes to find that a notion of free entropy exists in counterpart to the Shannon entropy. In fact there is a useful notion of free entropy. However, the development of this new concept is at present far from complete. The current state of affairs is that there are two distinct approaches to free entropy. These should give isomorphic theories, but at present we only know that they coincide in a limited number of situations.