Internal energy transfer is one of the most principal processes in the dynamic universe, but its exact thermodynamic processes have not been completely unveiled. We here propose an internal energy transfer theory for thermodynamic non-equilibrium, quasi-equilibrium, and equilibrium as a new paradigm for internal energy transfer, based on the first and the second laws of thermodynamics. The internal generation mechanisms of heat, work, and chemical energy transfer are considered. The internal energy fluxes are obtained as functions of temperature, pressure, chemical potential, time, and displacement under a postulate that the intensive variables are independent and orthogonal in extended phase spaces. The internal energy transfer theory is applicable to exploring the internal equilibrium, internal convection, external convection, and diffusion (or conduction) transfer mechanisms of heat, work, and chemical energy. The theory is a statistical thermodynamic generalization of thermal, mechanical, and chemical energy transfer as well as the conventional convection energy transfer. Six phase spaces consist of three intensive property dimensions of temperature, pressure, and chemical potential and three extensive property dimensions of entropy, volume, and particle number. The theory is a non-equilibrium generalization beyond the quasi-equilibrium theories of isothermal, isentropic, isobaric, isochoric, migration, and diffusion processes. (c) 2014 Elsevier Ltd. All rights reserved.