Clausius generalized the mathematical expression of Carnot’s principle obtained by Kelvin, and in 1865, introduced the concept of entropy and formulated the entropy principle. With the concept of entropy and the idea of the entropy principle, a definition of heat can be given, as well as mathematical formalism on equilibrium thermodynamics was formulated for organizing empirical data of thermodynamic properties. The establishment of the entropy principle signaled the beginning of a new era—in which, thermodynamics, which had originated as a branch of engineering knowledge, separated into two distinctive streams. The new science stream was manifested in the mathematical formalism on equilibrium thermodynamics. It is noted that the entropy principle, rather than the energy principle, is the true universal principle.