Stochastic Foundations of Atmospheric Thermodynamics: Deriving the Laws from Maximum Entropy and Implications for Earth’s Climate

A novel axiomatic foundation of entropy has recently been proposed, overcoming the limitations of classical and information-theoretic entropy foundations and eventually unifying probabilistic and physical entropy. A new set of postulates leads to a rigorous, uncertainty-based definition of entropy consistent with the principle of maximum entropy. Entropy is thus a purely stochastic concept quantifying uncertainty, thereby enriching Kolmogorov’s probability system. Applied to gas thermodynamics, the new framework reproduces classical results and derives, rather than assumes, the laws of thermodynamics. In atmospheric applications, entropy maximization yields an isothermal state as the molecular equilibrium. Gravitation does not alter the isothermal state but differentiates it from the isentropic one of macroscopic air parcels, whose motion drives the atmosphere away from equilibrium. Radiatively active gases, through interactions with shortwave and longwave radiation, sustain non-equilibrium vertical profiles of the atmospheric variables. Combined with the Stefan–Boltzmann law, these mechanisms provide a simple, parsimonious, and coherent explanation of observed atmospheric behaviors and the climatic system. The framework highlights thermodynamics as emergent from stochastics, offering new insights into molecular uncertainty, emergence of macroscopic structures, and radiation in shaping Earth’s climate. It also suggests a broader stochastic view of nature and atmospheric processes.