Fractal and Trans-scale Nature of Entropy: Towards a Geometrization of Thermodynamics develops a new vision for entropy in thermodynamics by proposing a new method to geometrize. It investigates how this approach can accommodate a large number of very different physical systems, going from combustion and turbulence towards cosmology. As an example, a simple interpretation of the Hawking entropy in black-hole physics is provided. In the life sciences, entropy appears as the dr