In this paper we formulate the foundation of extended irreversible thermodynamics by means of the generalized problem of the Boltzmann equation. First, by the generalized problem we obtain the set of evolution equations for the thermodynamic variables as well as a fundamental equation. This fundamental equation is intimately related to the laws of thermodynamics. Second, by the maximum entropy principle we construct the one-particle distribution function in exponential form and obtain the generalized Gibbs formula. Finally, we show that the fundamental equation ultimately gives rise to the generalized entropy balance equation.
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