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Irreversibility (that is, the "one-sidedness" of time) of a physical process can be characterized by using Lyapunov functions in the modern theory of stability. In this theoretical framework, entropy and its production rate have been generally regarded as Lyapunov functions in order to measure the irreversibility of various physical processes. In fact, the Lyapunov function is not always unique. In the represent work, a rigorous proof is given that the entransy and its dissipation rate can also serve as Lyapunov functions associated with the irreversibility of the heat conduction process without the conversion between heat and work. In addition, the variation of the entransy dissipation rate can lead to Fourier's heat conduction law, while the entropy production rate cannot. This shows that the entransy dissipation rate, rather than the entropy production rate, is the unique action for the heat conduction process, and can be used to establish the finite element method for the approximate solution of heat conduction problems and the optimization of heat transfer processes.

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High energy dual-energy X-ray Digital Radiography(DR) imaging is mainly used in material recognition of the cargo inspection. We introduce the development history and the principle of the technology and describe the data process flow of our system. The system corrects original data to get the dual-energy transparence image. Material categories of all points in the image are identified by the classification curve which is related to the X-ray energy spectrum. For the calibration of classification curve, our strategy involves a basic curve calibration and a real-time correction devoted to enhance the classification accuracy. Image segmentation and denoising methods are applied to smooth the image. The image contains more information after colorization. Some results show that our methods achieve the desired effect.