Free Analog of Pressure and Its Legendre Transform

The free analog of the pressure is introduced for multivariate noncommutative random variables and its Legendre transform is compared with Voiculescus microstate free entropy.Supported in part by Grant-in-Aid for Scientific Research (C)14540198 and by the program R&D support scheme for funding selected IT proposals of the Ministry of Public Management, Home Affairs, Posts and Telecommunications.