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

ILASOL 2013, WIS, Israel

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

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.

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 galaxyfp = the fraction of those stars that have planetsne = the average number of planets that can potentially support life per star that has planetsfl = the fraction of planets that could support life that actually develop life at some pointfi = 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

spaceL = the length of time for which such civilizations are able to release detectable signals into space

Drake’s Equation: N = R* ∙ fp ∙ ne ∙ fl ∙ fi ∙ fc ∙ L

ReferenceDrake, F., & Sobel, D. 1961, Is anyone out there?, NY: Delacorte Press

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

where

L = tf - tc

t0 = the beginning of the biospheretc = the beginning of communicationtf = the civilization’s end

N = R* ∙ fp ∙ ne ∙ fl ∙ fi ∙ fc ∙ L

Making

t0 earliertf laterand/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.

Animal Behaviour 86, (2013) 685–696

An analogy: Different reaction-times across Earth organisms

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.

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.

Consider, e.g., the greater biodiversity, i.e., emergence of new species, in tropical zones,

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?

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

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?

The Four Basic Parameters

1. Space (volume or even surface)

2. Time

3. Matter (number of particles)

4. Energy

Increase one or more of the other three and (2) will become considerably smaller!

Evolution’s rate is a function of the probabilities for appropriate mutations and interactions with the environment, which probabilities trivially require

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:

1( )dS dU PdV dN

T

The preferable probability density f that maximizes entropy on a set S, should satisfy:

1.

2.

3.

( ) 0 with equality outside Sf x

( ) 1S

f x dx

1( ) ( ) under constraints ,...,i i mS

f x r x dx

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

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.

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.

We will start with a simple toy-model:

A B ,C D C D

KA B

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.

1 [ ]d Cr

dt

Physical bounds

Theoretical Bounds on information

0 10,000T K

18

30 10

kg

m

410 3 10E J

Life is very loosely bounded. We aren’t imaginative enough!

Computational bounds (Lloyd)

Theoretical Bounds on information

505 10 / secOperations kg

164 10 /Memory bits kg 42 27 10 / secCommunication bits kg m

S. Lloyd, “Ultimate physical limits to computation”, http://arxiv.org/abs/quant-ph/9908043

Michaelis-Menten Kinetics

When an enzyme acts on substrate A, the rate can be modeled to

change according to:max

1\2

[ ]

[ ] [ ]

r Ar

A A

Which may result again in acceleration of the reaction rate.

(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.

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: ( )[ '] [ ']r k T A B

(3) Matter

Using van ‘t Hoff equation:

2

1 2 1

1 1ln ( )

K H

K R T T

We see that in endothermic reactions ( ), increasing T from T1 to T2 will also increase the equilibrium constant from K1 to K2, that is, more products will be created.

Also, according to Arrhenius equation the rate grows when increasing T.

0H

/aE RTr e

(best measured by temperature)

(4) Energy

ConclusionsTime 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.

(2) Time

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”