A novel stochastic foundation of entropy and its applicability to hydrometeorology

In the framework of the books "Stochastics of Hydroclimatic Extremes" and "Stochastics as Physics", a novel stochastic foundation of entropy is introduced. Entropy is treated as a purely probabilistic concept — a rigorous quantification of uncertainty — derived entirely within probability theory and stochastic processes, without deterministic or metaphorical interpretations. It emerges naturally from the principle of maximum entropy, unifying thermodynamic origins with statistical descriptions of complex systems. This approach allows key properties in atmospheric thermodynamics to be derived deductively, without presupposing thermodynamic principles. In hydrometeorology, it supports robust inference under uncertainty (by both deduction and induction), improved stochastic simulation of extremes, and a deeper understanding of long-term variability and climate dynamics through entropy extremization constrained by conservation laws. Applications illustrate the linkage between micro-scale stochastic behaviour and macro-scale hydrometeorological responses, offering a coherent physical-stochastic paradigm for geophysical systems.