In the present paper, the Brillouin formalism is shown to be able to be used within the entropy description of the knowledge acquisition processes, if the proper knowledge would be considered as a system transferring from the initial state to the final one. Then the cognition process just reflects decreasing the system (knowledge) entropy, and the information quantity, corresponding to such a decreasing of the entropy. Within the framework, in the paper the notion of the generalized entropy is improved and the researcher trend to decrease maximally the uncertainty of the final system (knowledge) state is just the minimization rather than maximization of such a generalized entropy. The interpretation of the Brillouin formalism enables one also to introduce, in accordance to the Cauchy-Schwarz inequality, the entropy-based coefficient of knowledge acquisition (ECKA) characterizing both the degree of the knowledge “depth” achieved by the researcher, as well as the “structure” of the knowledge. The values of such the ECKA lie within the interval from zero to unity, with the maximal value being just achieved at the exhaustive level of the researcher knowledge completeness. The paper has been supported by a grant of the Russian Foundation for Basic Researches (RFBR): project 12-08-01205-a.