Fractal and trans-scale nature of entropy: towards a geometrization of thermodynamics

Fractal and Trans-scale Nature of Entropy: Towards a Geometrization of Thermodynamics develops a new vision for entropy in thermodynamics by proposing a new way to geometrize the concept of entropy. It is based on a specific geometry which would be the spatial support for entropy, a geometry called entropic skins geometry, where the fundamental components of a general thermodynamical process are surfaces or lines having some specific multi-scale geometries. The authors investigate how this approach can accommodate a large number of very different physical systems, going from combustion and turbulence towards cosmology. The authors propose, for instance, a simple interpretation of the Hawking entropy in black-hole physics. The geometrical concepts developed can also provide a new way to consider ecosystems, urban dynamics and human cognition. The authors show that this leads to an original and positive interpretation of entropy which today is lacking. In life sciences, entropy appears as the driving element for the organization of systems; this book aims to demonstrate this fact via simple pedagogical tools. We will show that entropy cannot be interpreted as a basic measure of disorder anymore but rather as the measure of the dispersion of energy and of its capacity to form structure and organization. Explores the strong link between geometry and thermodynamicsOffers an original understanding of entropyExplains how to visualize phenomena where thermodynamics and entropy are important in the optimization of thermal machines but also in other fields such as nanophysics, life sciences or astrophysicsExplains entropy in thermodynamics through fractal geometry and more generally with trans-scale geometries