The paper intends to contribute to a better understanding of the phenomenon of scientific capital. Scientific capital is a well-known concept for measuring and assessing the accumulated recognition and the specific scientific power. The concept of scientific capital developed by Pierre Bourdieu is used in international social science research to explain a set of scholarly properties and practices. Mathematical modeling is applied as a lens through which to address the scientific capital. The principal contribution of this paper is an axiomatic characterization of scientific capital in terms of natural axioms. The application of the axiomatic method to scientific capital reveals novel insights into problem still not covered by mathematical modeling. Proposed model embraces the interrelations between separate sociological variables, providing a unified sociological view of science. Suggested micro variational principle is based upon postulate, which affirms that (under suitable conditions) the observed state of the agent in a scientific field maximizes scientific capital. Its value can be roughly imagined as a volume of social differences. According the considered macro variational principle, the actual state of a scientific field makes so-called energy functional (which is associated with the distribution of scientific capital) minimal.