**1. Introduction**

Earth's atmosphere is an open system far from equilibrium, both physically – there is vigorous circulation, and chemically – for example, the methane/oxygen ratio is some 30 orders of magnitude larger than the equilibrium value. It is not isolated; there are varying fluxes of photons in and out, water exchanges on a 10-day time scale with the oceans, carbon dioxide, many organic molecules, nitrous oxide, methane, methyl chloride, ammonia and sulphurous compounds are subject to biogeochemistry at both land and sea surfaces. Long-lived molecules such as chlorofluoromethanes (50–100 years) can be re-emitted from both land and sea, and even the major constituents, O2 (order 104 years) and N2 (order 106 years) are cycled by geochemistry, biochemistry and lightning. Last but not least, condensed matter in the form of aqueous aerosols is produced by gas to particle conversion, by clouds and from sea spray, and which serve as condensation nuclei for cloud droplets, ice crystals and precipitation. The air-water interface is an important reaction venue [1], and often accelerates reactions [2–6]. Some or all of these molecules and particles affect the transmission of both solar visible and ultraviolet and terrestrial infrared radiation, and consequently are central to the maintenance of atmospheric temperature.

Since the atmosphere is so far from equilibrium, standard statistical thermodynamics calculable by quantal chemical techniques are not applicable, either in the air or aerosols. The thermodynamic formulation of statistical multifractals has been shown to be a mapping, not just a formal coincidence by Lovejoy and Schertzer [7], following their analyses of atmospheric variables as statistical multifractals [8, 9]. It has been used to demonstrate, by analysis of observations, that the current global

heating is attributable almost wholly to carbon dioxide emissions from fossil fuel burning [10]. Note that this is a numerical model-independent result. By combining these analyses with results from molecular dynamics calculations [11] it has been shown that atmospheric turbulence is an emergent property of molecular gas populations in an asymmetric environment, scale invariant over the 15 orders of magnitude in length scale, from the mean free path at surface pressure to a great circle [5, 12, 13]. The scale invariance approach to atmospheric thermodynamics has been successfully applied to aircraft data from the stratosphere [14] and combined with theoretical and experimental results for aerosol particles to form a potential pathway to understanding and exploiting the observed acceleration of many chemical reactions, some of them atmospheric chemical, in and on microdroplets compared to their slower or non-occurrent behaviour in bulk fluid [5]. Microdroplet surfaces are where free energy is concentrated, even in a pure homogeneous droplet, as surface tension. So, for both gaseous composition chemistry and the aerosol population, analysis can be attempted with this approach. All these factors are directly relevant to the calculation of global heating under anthropogenic perturbations. The issue is examined in the rest of the chapter by this scale invariant thermodynamics approach. A useful review of energy production and its interaction with the environment is given in Goede et al. [15]. Further considerations are in Refs. [16–18].

The above approach provides perspective on geoengineering by "solar radiation management" when combined with the complexities of aerosol particles in the lower stratosphere [19]. Because of dissipation by infrared radiation to space, any method of reducing global heating by fossil fuel burning cannot be powered by combustion of coal, oil and gas: renewable sources must be deployed.
