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Maxwell\'s Demon: Implications for Evolution and Biogenesis

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Maxwell\'s Demon: Implications for Evolution and Biogenesis

Avshalom C. ElitzurIyar, The Israeli Institute for Advanced Research

Copyleft 2010

The Relevance of Thermodynamicsto Life Sciences

- Thermodynamics is a discipline that studies energy, entropy, and information

Brillouin’s Information:Information=(Initial Uncertainty)–(Final Uncertainty)

For several equally possible states, P0

With information reducing the possible states to P1:

Ideally, for P1=1:

Shannon’s Information:Uncertainty = Entropy

Boltzmann’s Entropy

For all states being equiprobable:

Otherwise:

Information of one English letter:

For a string of G letters:

The Relevance of Thermodynamicsto Life Sciences

- Thermodynamics is a discipline that studies energy, entropy, and information
- Its jurisdiction is ubiquitous, regardless of the system’s chemical composition or type of energy

Whence the entropy differencebetween animate and inanimate systems ?

The Common Textbook Answer:

“Living organisms are open systems”

?

Adaptation = Information

Attempts at Exorcizing

- Kelvin: The devil is alive
- Von Smoluchowski: It’s intelligent
- Szilard, Brillouin: It uses information
- Bennett & Landauer: It erases information

Information and Energy

Information Costs Energy

ergo

Information can Save Energy

With information, you can do work with less energy, applied at the right time and/or place

“Less energy, at the right time/place”:Comparison between two methods of kill

Minute chemical energy: Neurotoxin (cobrotoxin) moleculesreach the synapses with enormous precision

Considerable mechanical energy: Crushing the entire prey’s body

Et

Ec

Ee

Et

Ec + Ee

Ec + Ee

Ec\'>Ec

Ek

The Demon Vs. the Living Organism: The Analogy

Life increases energy’s efficiency, up the thermodynamic scale

It does that with the aid of information

The Demon Vs. the Living Organism: The Disanalogy

The real environment is never completely disordered but complex

The organism does not create order but complexity

Ordered, Random, Complex

Measures of Orderliness

- Divergence from equiprobability (Gatlin) (Are there any digits in the sequence that are more common?)
- Divergence from independence (Gatlin) (Is there any dependence between the digits?)
- Redundancy (Chaitin) (Can the sequence be compressed into any shorter algorithm?)
- 3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
- 1860271194945955774038867706591873856869843786230090655440136901425331081581505348840600451256617983
- 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789
- 6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374

Bennett’s Measure of Complexity

Given the shortest algorithm, how much computation is required to produce the sequence from it?And conversely:How much computation is required to encode a sequence into its shortest algorithm?

complexity

Low order

High order

The Ski-Lift Pathway: Thermodynamically Unique, Biologically UbiquitousGoren Gordon & Avshalom C. Elitzur

High Order

Requires

Energy

Spontaneous

Low Order

How do you get to some desired state?

High Order

Step 1:

Use Ski-Lift, get to the top

Requires

Energy

Spontaneous

Initial State

Desired State

Low Order

How do you get to some desired state?

High Order

Step 1:

Use Ski-Lift, get to the top

Requires

Energy

Spontaneous

Initial State

Desired State

Low Order

How do you get to some desired state?

High Order

Step 1:

Use Ski-Lift, get to the top

Requires

Energy

Spontaneous

Step 2:

Ski down

Initial State

Desired State

Low Order

The Ski-Lift Conjecture (Gordon & Elitzur, 2009):

Life approaches complexity “from above,” i.e., from the high-order state, and not “from below,” from the low-order state. Though the former route seems to require more energy, the latter requires immeasurable information, hence unrealistic energy.

Dynamical evolution of complex states

How to reach a complex state?

- Direct path
- Probabilistic
- Deterministic
- Ski-lift theorem

Ski-lift

Entropy

Final state

Initial state

Direct path

Perform a transformation on the initial state to arrive at the final state

Ti!f (???)

Initial state unknown

For each transformation

only one initial state transforms

to final state

Hilbert Space

Initial state

Final state

Perform a transformation on the initial state to arrive at the final state

Ti!f (???)

Initial state unknown

For each transformation

only one initial state transforms

to final state

Hilbert Space

Perform transformation once

Energy cost:

E=

Probability of success:

P=1/Ni=e-S(i)¿ 1

Initial state

Final state

Perform a transformation on the initial state to arrive at the final state

Ti!f (???)

Initial state unknown

For each transformation

only one initial state transforms

to final state

Hilbert Space

Repeat transformation until final

state is reached

Probability of success:

P=1

Average energy cost:

E= eS(i)À 1

Initial state

Final state

Perform a transformation on the initial state to arrive at the final state

Ti!f

If one has information about initial state

Ii=S(i)

And information about final state (environment)

If=S(f)

Then can perform the

right transformation once

Probability of success:

P=1

Energy cost:

E=

Information required:

I=S(i)+S(f)

Hilbert Space

Initial state

Final state

Two stages path:

Stage 1: Increase order

S-i! order

Ends with a specific, known state

Probability of success: P1=1

Energy cost: E1=S(i)

Hilbert Space

Initial state

Final state

Two stages path:

Stage 1: Increase order

S-i! order

Ends with a specific, known state

Probability of success: P1=1

Energy cost: E1=S(i)

Hilbert Space

Stage 2: Controlled transformation

Torder!f

Ends with the specific, final state

Probability of success: P2=1

Energy cost: E2=

Initial state

Final state

Requires information on final state (environment), in order to apply

the right transformation on ordered-state

Probability of success:

P=1

Energy cost:

Eski-lift=S(i)+

Information required:

I=S(f)

Hilbert Space

Initial state

Final state

Direct Path

Probabilistic

Low probability

Low energy

Deterministic:

High probability

High energy

Information:

Requires much information

Low energy

Ski-lift

Deterministic

Controlled

Reproducible

Costs low energy

Requires only environmental information

Comparison between pathsSki-lift uses ordered-state and environmental information

to obtain controllability and reproducibility

Bennett’s Measure of Complexity

Given the shortest algorithm, how much computation is required to produce the sequence from it?And conversely:How much computation is required to encode a sequence into its shortest algorithm?

complexity

Low order

High order

Biological examples

- Cell formation
- Apoptosis
- Embryonic development
- Ecological development

The Morphotropic State as the Cellular Progenitor of Complexity

Minsky A, Shimoni E, Frenkiel-Krispin D. (2002) “Stress, order and survival.”Nat. Rev. Mol. Cell Biol. Jan;3(1):50-60.

Order as the Ecological Progenitor of Complexity

Maintaining the complexity of civilization necessitates

huge reservoirs of order

Schrödinger’s “What is life?” revisited

Hilbert Space

Requires energy

High entropy

High information

High order

Redundancy

High complexity

(specific environment)

Requires information

- Leff, H. S., & Rex, A. F. (2003) Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing. Bristol: Institute of Physics Publishing.
- Dill, K.A. , & Bromberg, S. (2003) Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology. New York: Garland Science.
- Di Cera, E., Ed. (2000) Thermodynamics in Biology” Oxford: Oxford University Press.
- Gordon, G., & Elitzur, A. C. (2008) The Ski-Lift Pathway: Thermodynamically unique, biologically ubiquitous. http://www.a-c-elitzur.co.il/site/siteArticle.asp?ar=214

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