Logarithmic Generalization of the Lambert W function and its Applications to Adiabatic Thermostatics of the Three-Parameter Entropy

TL;DR

This paper introduces a logarithmic generalization of the Lambert W function, explores its mathematical properties, and applies it to analyze the thermostatics of a three-parameter entropy model for ideal gases.

Contribution

It presents a new logarithmic Lambert function, derives its properties, and applies it to solve thermostatics problems in classical ideal gases with three-parameter entropy.

Findings

Derived the derivative, integral, and Taylor series of the logarithmic Lambert function.

Expressed heat functions in terms of the new function.

Applied the function to thermostatics of ideal gases with three-parameter entropy.

Abstract

A generalization of the Lambert W function called the logarithmic Lambert function is found to be a solution to the thermostatics 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 thermostatics are computed and the heat functions are expressed in terms of the logarithmic Lambert function.