Natural Selection and Scale Invariance.

This review points out that three of the essential features of natural selection-competition for a finite resource, variation, and transmission of memory-occur in an extremely simple, thermalized molecular population, one of colliding "billiard balls" subject to an anisotropy, a directional flux of energetic molecules. The emergence of scaling behavior, scale invariance, in such systems is considered in the context of the emergence of complexity driven by Gibbs free energy, the origins of life, and known chemistries in planetary and astrophysical conditions. It is suggested that the thermodynamic formalism of statistical multifractality offers a parallel between the microscopic and macroscopic views of non-equilibrium systems and their evolution, different from, empirically determinable, and therefore complementing traditional definitions of entropy and its production in living systems. Further, the approach supports the existence of a bridge between microscopic and macroscopic scales, the missing mesoscopic scale. It is argued that natural selection consequently operates on all scales-whether or not life results will depend on both the initial and the evolving boundary conditions. That life alters the boundary conditions ensures nonlinearity and scale invariance. Evolution by natural selection will have taken place in Earth's fluid envelope; both air and water display scale invariance and are far from chemical equilibrium, a complex condition driven by the Gibbs free energy arising from the entropy difference between the incoming solar beam and the outgoing infrared radiation to the cold sink of space acting on the initial conditions within evolving boundary conditions. Symmetry breaking's role in the atmospheric state is discussed, particularly in regard to aerosol fission in the context of airborne bacteria and viruses in both current and prebiotic times. Over 4.4 billion years, the factors operating to support natural selection will have evolved along with the entire system from relative simplicity to the current complexity.

Proposed Empirical Entropy and Gibbs Energy Based on Observations of Scale Invariance in Open Nonequilibrium Systems.

There is no widely agreed definition of entropy, and consequently Gibbs energy, in open systems far from equilibrium. One recent approach has sought to formulate an entropy and Gibbs energy based on observed scale invariances in geophysical variables, particularly in atmospheric quantities, including the molecules constituting stratospheric chemistry. The Hamiltonian flux dynamics of energy in macroscopic open nonequilibrium systems maps to energy in equilibrium statistical thermodynamics, and corresponding equivalences of scale invariant variables with other relevant statistical mechanical variables such as entropy, Gibbs energy, and 1/(kBoltzmannT), are not just formally analogous but are also mappings. Three proof-of-concept representative examples from available adequate stratospheric chemistry observations-temperature, wind speed and ozone-are calculated, with the aim of applying these mappings and equivalences. Potential applications of the approach to scale invariant observations from the literature, involving scales from molecular through laboratory to astronomical, are considered. Theoretical support for the approach from the literature is discussed.

Ocean-atmosphere interactions in the emergence of complexity in simple chemical systems.

The prebiotic conversion of simple organic molecules into complex biopolymers necessary for life can only have emerged on a stage set by geophysics. The transition between "prebiotic soup," the diverse mixture of small molecules, and complex, self-replicating organisms requires passing through the bottleneck of fundamental chemistry. In this Account, we examine how water-air interfaces, namely, the surfaces of lakes, oceans, and atmospheric aerosols on ancient Earth, facilitated the emergence of complex structures necessary for life. Aerosols are liquid or solid suspensions in air with a broad, power law size distribution. Collectively, these globally distributed atmospheric particles have an enormous surface area. Organic films at the interface between water and air offer advantages for biomolecular synthesis compared with the bulk and can simultaneously participate in the folding of biopolymers into primitive enclosed structures. We survey the advantages of the water-air interface for prebiotic chemistry in a geophysical context from three points of view. We examine the formation of biopolymers from simple organic precursors and describe the necessity and availability of enclosures. In addition, we provide a statistical mechanical approach to natural selection and emergence of complexity that proposes a link between these molecular mechanisms and macroscopic scales. Very large aerosol populations were ubiquitous on ancient Earth, and the surfaces of lakes, oceans, and atmospheric aerosols would have provided an auspicious environment for the emergence of complex structures necessary for life. These prebiotic reactors would inevitably have incorporated the products of chemistry into their anhydrous, two-dimensional organic films in the three-dimensional fluids of the gaseous atmosphere and the liquid ocean. The untrammeled operation of natural selection on these aerosols provided the likely location where condensation reactions could form biopolymers by elimination of water. The fluctuating exposure of the large, recycling aerosol populations to radiation, pressure, temperature, and humidity over geological time allows complexity to emerge from simple molecular precursors. We propose an approach that connects chemical statistical thermodynamics and the macroscopic world of the planetary ocean and atmosphere.

Molecular velocity distributions and generalized scale invariance in the turbulent atmosphere.

Airborne observations of ozone, temperature and the spectral actinic photon flux for ozone in the Arctic lower stratosphere April-September 1997 and January-March 2000 allow a connection to be made between the rate of production of translationally hot atoms and molecules via ozone photodissociation and the intermittency of temperature. Seen in the context of non-equilibrium statistical mechanics literature results from molecular dynamics simulations, the observed correlation between the molecular scale production of translationally hot atoms and molecules and the macroscopic fluid mechanical intermittency of temperature may imply a departure from Maxwell-Boltzmann distributions of molecular velocities, with consequences for chemistry, radiative line shapes and turbulence in the atmosphere, arising from overpopulated high velocity tails of the probability distribution functions (PDFs).