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The concept of entransy developed in recent years can describe the heat transport ability. This paper extends this concept to the open thermodynamic system and defines the concept of enthalpy entransy. The entransy balance equation of steady open thermodynamic systems, as well as the concept of entransy loss, is developed. The entransy balance equation is applied to analyzing and discussing the air standard cycle. It is found that the entransy loss rate can describe the change in net power output from the cycle but the entropy generation rate cannot when the heat absorbed by the working medium is from the combustion reaction of the gas fuel. When the working medium is heated by a high temperature stream, both the maximum entransy loss rate and the minimum entropy generation rate correspond to the maximum net power output from the cycle. Hence, the concept of entransy loss is an appropriate figure of merit that describes the cycle performance. As nearly 80% of the total energy consumption is related to heat [1], the optimization design of heat transfer and heatwork conversion has become one of important research topics under the increasing requirements on reducing energy consumption. For instance, the design optimization could improve the performance of heat exchangers and increase heat transfer rate [1]. Optimizing the thermal conductance distribution of the heat exchanger groups could also increase the work output in heat-work conversion [2]. Several theories have been developed for the optimal design of heat transfer and heat-work conversion in recent years [1][2][3][4][5][6][7]. Bejan [4-6] developed the constructal theory and thermodynamic optimizations for heat transfer processes. In heat conduction optimization of the Volume-to-Point problem, Bejan [4] developed the constructal theory, in which the basic, imagined structure of the high conductivity material is given, and the aspect ratio of the structure is optimized through theoretical derivation and numerical simulation to decrease the highest temperature of the heated domain. The sub-structure, third degree structure, etc. are evolved to cover the whole domain. The constructal theory was found to be effective for heat conduction optimization and was extended to heat convection optimizations [8][9][10]. Furthermore, Bejan [4-6] related the optimal heat transfer to the minimum production of entropy generation and extended this idea into other systems. Researchers have done many investigations on heat transfer optimization based on the minimum principle of entropy generation [11,12]. As the objective of this kind of optimization method is to minimize the entropy generation, it is called thermodynamic optimization.However, there are arguments on the constructal theory and thermodynamic optimization in heat transfer [6,[13][14][15][16][17]. Ghodoossi [13,14] applied the constructal theory to analyzing the effect of the complexity levels of the tree network of conducting paths and found that the heat flow performance does not essentially improve if the intern...

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