E-infinity as a fiber bundle and its thermodynamics

This paper presents a novel approach for the investigation of fractals. Using parameters of fractal organization we introduce generalized Gibbs statistic and apply it for the development of thermodynamics of fractals. Our generalization is based on a fractal generation function that produces a representation for particular states of fractal space–time. All considerations are embedded into the framework of E-infinity theory viewed as a fiber bundle. Nevertheless El Naschie’s space–time represents a particular case of undistorted fractal state which corresponds to the equilibrium state of fractal space–time in our theory. Related topics of thermodynamics of fractals are discussed.