Closure relations problem of hydrodynamical models in semiconductors is considered by expressing third- and fourth-order closure relations for the moments of the distribution functionin terms of second-order Lagrange multipliers using a generalized Maxwell-Boltzmann distributionfunction within information theory. Calculation results are commented and compared withothers to justify the accuracy of the approach developed in this paper. The comparison involves,in the first part with good agreements, the closure relations results obtained within extendedthermodynamics which were checked by means of Monte Carlo simulations, in the second part,the results obtained by Grad's method which expands the distribution function up to fourth-orderin Hermite polynomials. It is seen that the latter method cannot give any restriction on closurerelations for higher-order moments, within the same conditions proposed in our approach. Theimportant role of Lagrange multipliers for the determination of all closure relations is asserted.
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