Analogies between electric, hydraulic, and thermal quantities do exist for developing various circuit models that involve quantities such as currents and voltages, flows and pressures, and heat transfers and temperatures. With the increasing interest in multi-carrier energy systems, it would be beneficial to extend the scope of analogies to the enthalpy transfer by advection. The presentation of the concept and the realization of this analogy extension are the purpose of this paper. It is shown how the enthalpy transfer is formulated using circuit equivalents and how they can be used in the modeling of components such as junctions and pipes of multi-carrier energy systems. The theoretical considerations are complemented by validation through comparison with software models and physical experiment. The value of implementing the enthalpy transfer using circuit equivalents is illustrated by the modeling of a combined heat and power multi-carrier energy system implemented in a nodal-analysis-based network simulator of the EMTP type.