Logarithmic Generalization of the Lambert W Function and Its Applications to Adiabatic Thermostatistics of the Three-Parameter Entropy

A generalization of the Lambert W function called the logarithmic Lambert function is introduced and is found to be a solution to the thermostatistics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula, and branches of the function are obtained. The heat functions and specific heats are computed using the “unphysical” temperature and expressed in terms of the logarithmic Lambert function.