Entropy of fractal systems
The Kolmogorov entropy is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase point on the attractor. Numerically, the Kolmogorov entropy can be estimated as the Rnyi entropy. A special case of Rnyi entropy is the information theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant is the thermodynamic entropy. Fractal structures are characterized by their fractal dimension. There exists an infinite family of fractal dimensions. A generalized fractal dimension  can be defined in an E E -dimensional space. The Rnyi entropy and generalized fractal dimension are connected by a straight relation.
kolmogorov entropy rnyi entropy shannon entropy thermodynamic entropy fractal dimension fractal physics fractal geometry fractal measure