How Fast Can Life Evolve? Thermodynamic Notes on the last Term in Drake’s Equation

1. How Fast Can Life Evolve? Thermodynamic Notes on the last Term in Drake’s Equation Eliahu Coheneliahuco@post.tau.ac.il Renan Grossrenan.gross@gmail.com Boaz Tamirboaz_tamir@post.bezalel.ac.il Avshalom C. Elitzur*avshalom@iyar.org.il ILASOL 2013, WIS, Israel

2. ABSTRACT Prevalent estimates for the likelihood of extraterrestrial life seem to take it for granted that the time needed for its emergence and evolution is of the scale known from Earth, i.e. some billion years. We challenge this implicit assumption. From the thermodynamic viewpoint, a biosphere’s entropy exchanges with its environment depend on the availability of the four basic physical resources, namely matter, energy, space and time. Should one or more of the former three be more abundant, the time factor can be by far shorter. For example, an Earth-like planet is conceivable of greater volume and/or larger amounts of available chemicals and/or free energy. In such an environment, evolution may proceed orders of magnitude faster than on Earth. Hence even under slightly varied conditions, even more extreme “overnight” scenarios are possible. We propose some exploratory estimates of these possibilities together with a new set of physical limitations and their main consequences. Finally we point out some directions for more extensive works.

3. Drake’s Equation: N = R* ∙ fp ∙ ne ∙ fl ∙ fi ∙ fc ∙ L where N = the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone); R*= the average rate of star formation in our galaxy fp= the fraction of those stars that have planets ne= the average number of planets that can potentially support life per star that has planets fl= the fraction of planets that could support life that actually develop life at some point fi= the fraction of planets with life that actually go on to develop intelligent life (civilizations) fc= the fraction of civilizations that develop a technology that releases detectable signs of their existence into space L = the length of time for which such civilizations are able to release detectable signals into space ReferenceDrake, F., & Sobel, D. 1961, Is anyone out there?, NY: Delacorte Press

4. Shortcomings: … Relies on 21st-century physics (i.e. taking QM, GR and present-day cosmology as the definitive description of the universe), Hence assumes the resulting limits on technology (e.g., space and time limitations) Assumes Earth-like life (carbon-based, etc.) Hence takes the 4-billion-years scale for granted

5. N = R* ∙ fp ∙ ne ∙ fl ∙ fi ∙ fc ∙ L where L = tf - tc t0 = the beginning of the biosphere tc = the beginning of communication tf = the civilization’s end

6. Making • t0earlier • tflater • and/or • tc closer to t0 (i.e. life starting earlier, ending later and evolving faster) Would make L = tf -tc and thereby N much larger* *Provided that the civilization evolved from it is not self-destructive, indifferent to other life forms, etc.

7. An analogy: Different reaction-times across Earth organisms Animal Behaviour 86, (2013) 685–696

8. Can we conceive of an entire biosphere whose evolution is much faster than ours like the fly’s reaction-time far surpassing* ours? * Well, most of the time.

9. Consider, e.g., the greater biodiversity, i.e., emergence of new species, in tropical zones, Kier, G., Kreft, H., Lee, T.M., Jetz, W., Ibisch, P.I., Nowicki, C., Mutke, J. & Barthlott, W. (2009): A global assessment of endemism and species richness across island and mainland regions. - Proceedings of the National Academy of Sciences 106: 9322–9327.

10. Consider, e.g., the greater biodiversity, i.e., emergence of new species, in tropical zones, or the rapid speciation following mass extinctions,

11. Consider, e.g., the greater biodiversity, i.e., emergence of new species, in tropical zones, or the rapid speciation following mass extinctions, What if all Earth had a tropical climate, of endured more frequent extinctions?

12. Or consider the “Hot Origins of Life” hypothesis: M. Rossi, M. Ciaramella, R. Cannio, F. M. Pisani, M. Moracci, and S. Bartolucci (2002) Meeting review: Extremophiles 2002. Journal of Bacteriology 185: 3683-9. Again: What if Earth has never cooled? Wouldn’t the subsequent multicellular extremophiles evolve much faster under such energy abundance?

13. Evolution’s rate is a function of the probabilities for appropriate mutations and interactions with the environment, which probabilities trivially require The Four Basic Parameters Space (volume or even surface) Time Matter (number of particles) Energy Increase one or more of the other three and (2) will become considerably smaller!

14. The Analogous Measure: Entropy Looking for a physical parameter similarly based on probabilities and depending on energy, volume and the number of particles, we immediately encounter entropy. Indeed:

15. The preferable probability density f that maximizes entropy on a set S, should satisfy: 1. 2. 3.

16. Entropy’s Twin-Antagonists: Information, Complexity and Computation Life = a self-improving process, generally enabling • greater complexity • with the aid of greater amounts of environmental information, i.e., more advantageous mutations stored in the genome • Undergoing more efficient computation, i.e. greater precision in replication and genes recombination, etc. under constant natural selection. For achieving the ultimate goal of fighting local entropy increase

17. Entropy’s Twin-Antagonists: Information, Complexity and Computation They are related to entropy, hence depend on the same four basic ingredients, hence subject to the same restrictions. According to Landauer’s principle, any logically irreversible computation requires energy (at least kbTln2). Furthermore, computations use some memory storage which can potentially grow provided there are more available particles and space.

18. This however holds for thermodynamic equilibrium, while Life proceeds very far from equilibrium. However, for proving our point, it seems that understanding how equilibrium changes, when the system’s parameters change, will suffice.

19. We will start with a simple toy-model: Where A and B are two reactants, C is the main product and D is the side product. Later we will proceed to more complex models.

20. Theoretical Bounds on information Physical bounds Life is very loosely bounded. We aren’t imaginative enough!

21. Theoretical Bounds on information Computational bounds (Lloyd) S. Lloyd, “Ultimate physical limits to computation”, http://arxiv.org/abs/quant-ph/9908043

22. Michaelis-Menten Kinetics When an enzyme acts on substrate A, the rate can be modeled to change according to: Which may result again in acceleration of the reaction rate.

23. (1) Space Extreme situations are the most problematic: very high or very low volume will probably hinder life creation. Leaving the concentration of reactants high, while increasing the volume will enable more degrees of freedom and greater diversity of life forms. Compartmentalization: sometimes smaller volume is desirable.

24. (3) Matter It seems reasonable that when more building blocks are available, life would evolve faster. Indeed, according to Le Chatelier's principle, increasing the concentration of reactants will increase K. The rate will also increase according to:

25. (4) Energy (best measured by temperature) Using van ‘t Hoff equation: We see that in endothermic reactions ( ), increasing T from T1 to T2 will also increase the equilibrium constant from K1to K2, that is, more products will be created. Also, according to Arrhenius equation the rate grows when increasing T.

26. (2) Time Conclusions Time is only one out of four equally essential resources for life’s emergence and evolution. With the great likelihood for the other three to be much larger, there is nothing fundamental in the four-billion-years timescale. Basic thermodynamic considerations allow the emergence of an extraterrestrial biosphere “overnight” in comparison to ours.

27. Future Directions Much work is needed for quantifying the above claims Non-equilibrium thermodynamics Zhabotinsky-Belousov reaction Radiation-Diffusion More on life and information, “Chemical Computations”