Departures from thermal equilibrium in gases, when different temperatures characterize a mixture, arise in a wide range of industrial and academic applications. Therefore, the robust computation of linearly constrained, chemical equilibrium compositions for such mixtures in thermal non-equilibrium is an important topic for which numerous formulations have been developed. In this work, we present a Gibbs function continuation generalization for linearly constrained multi-temperature equilibrium calculations. The validity of the proposed method is analyzed and it is shown that the single temperature method arises as a special case of the multi-temperature algorithm when local thermal equilibrium is considered. We present three numerical test cases to demonstrate the validity range, accuracy and robustness of the model.
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