Publisher Summary This chapter focuses on the statistical applications of information energy. Applications to some related areas, such as solving logic problems, connections with hyperreal numbers, noiseless coding, etc., are also made. The chapter also analyzes the notion of information energy to the continuous case and examines some of its properties. The difference between the continuous and the discrete case is worth emphasizing—that is, the information energy in the continuous case is not a limit of the information energy in the discrete case. These differences between the discrete and continuous distribution warns that the results holding for the discrete case cannot be extended directly to the continuous case. They need independent verification. Furthermore, the chapter discusses the information energy of a point process. After studying the properties relative to the rate of change of information energy, it is proved that given the class of stationary point processes, the information energy is minimum for the Poisson process.