A significant improvement in electron mobility has been achieved by several authors on AlInGaN/GaN heterostructures by adding a small amount of Ga to the AlInN alloy. In this study, we propose that thermodynamic stability plays an important role in controlling the electron transport properties of these heterostructures. A quantitative investigation of the thermodynamic stability of the AlInGaN barrier has been carried out analytically, for a wide range of compositions (0.5 ≤ Al ≤ 0.8; In = 0.2, 0.15, 0.1). A slow change in the thermodynamic stability is observed when the Ga atoms replace only the Al atoms. In contrast, a significant improvement in thermodynamic stability is observed when the indium atoms are replaced by the Ga atoms in the same Al0.83In0.17N layer. It is found that the Al content in the range of 65%-70% with 10% In exhibits the highest thermodynamic stability within the calculated composition range owing to the significant reduction in total elastic strain in the barrier. Thereby, it leads to the highest electron mobility, as evidenced by the experimental observations in this work, i.e., electron mobility of 2090 cm2/V s with a sheet carrier density of 1.09 × 1013 cm-2. Therefore, the thermodynamic stability apart from commonly observed scattering mechanisms may at least be partially held to be responsible for the consistent improvement in electron mobility in AlInGaN/GaN heterostructures.