Investigation Of Thermodynamic Geometry And Christoffel Coefficients of Modified Chaplygin Gas Using Weinhold Metric

Abstract

In this article, the dynamic components and temperature values of modified Chaplygin gas, which has the equation of state P=Aρ-B/ρ^α were obtained as a function of entropy and volume for the universe filled with modified Chaplygin gas, first at α=0 and then at α=1. All symbols used in the derivation are defined explicitly, and the entropy-dependent integration functions are fixed through the thermodynamic relation T=(∂U/∂S)V. The original contribution of this work is the combined derivation of the Weinhold curvature and the corresponding Christoffel coefficients for modified Chaplygin gas within the same thermodynamic phase-space framework. The signs of the thermodynamic curvature (R=0, R>0, R<0) were interpreted only as thermodynamic-geometric indicators of the dominant interaction regime and were compared with the related literature. A numerical illustration is also included to show how the curvature sign changes with model parameters. Subsequently, all components of the Weinhold metric and the thermodynamic curvature for modified Chaplygin gas were obtained for both α=0 and α=1. Finally, the Christoffel coefficients were obtained on the Weinhold thermodynamic phase space for the same conditions.