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In the present interdisciplinary review we focus on the applications of thesymmetry principles to quantum and statistical physics in connection with someother branches of science. The profound and innovative idea of quasiaveragesformulated by N.N. Bogoliubov, gives the so-called macro-objectivation of thedegeneracy in domain of quantum statistical mechanics, quantum field theory andin the quantum physics in general. We discuss the complementary unifying ideasof modern physics, namely: spontaneous symmetry breaking, quantum protectorateand emergence. The interrelation of the concepts of symmetry breaking,quasiaverages and quantum protectorate was analyzed in the context of quantumtheory and statistical physics. The chief purposes of this paper were todemonstrate the connection and interrelation of these conceptual advances ofthe many-body physics and to try to show explicitly that those concepts, thoughdifferent in details, have a certain common features. Several problems in thefield of statistical physics of complex materials and systems (e.g. thechirality of molecules) and the foundations of the microscopic theory ofmagnetism and superconductivity were discussed in relation to these ideas.

Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence