Debates: Does Information Theory Provide a New Paradigm for Earth Science? Emerging Concepts and Pathways of Information Physics

Entropy and Information are key concepts not only in Information Theory but also in Physics: historically in the fields of Thermodynamics, Statistical and Analytical Mechanics, and, more recently, in the field of Information Physics. In this paper we argue that Information Physics reconciles and generalizes statistical, geometric, and mechanistic views on information. We start by demonstrating how the use and interpretation of Entropy and Information coincide in Information Theory, Statistical Thermodynamics, and Analytical Mechanics, and how this can be taken advantage of when addressing Earth Science problems in general and hydrological problems in particular. In the second part we discuss how Information Physics provides ways to quantify Information and Entropy from fundamental physical principles. This extends their use to cases where the preconditions to calculate Entropy in the classical manner as an aggregate statistical measure are not met. Indeed, these preconditions are rarely met in the Earth Sciences due either to limited observations or the far‐from‐equilibrium nature of evolving systems. Information Physics therefore offers new opportunities for improving the treatment of Earth Science problems. Key Points Information Physics reconciles and generalizes statistical, geometric, and mechanistic views on information and Entropy Statistical uncertainty stems from dynamic diversity and in turn from Entropy production, with information metrics having a physical meaning Information metrics can be developed to enable the study of far‐from‐equilibrium structural‐functional coevolution in hydrology and Earth system dynamics