Maxwell's Demon: Implications for Evolution and Biogenesis
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Maxwell's Demon: Implications for Evolution and Biogenesis Avshalom C. Elitzur Iyar, The Israeli Institute for Advanced Research. Copyleft 2010. The Relevance of Thermodynamics to Life Sciences . Thermodynamics is a discipline that studies energy, entropy, and information.

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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
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
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 difference between animate and inanimate systems
Whence the entropy differencebetween animate and inanimate systems ?

The Common Textbook Answer:

“Living organisms are open systems”

?


Open systems
Open Systems:

Rocks

Chairs

Blackboards

Trash cans (!)

etc.


The Thesis:

Adaptation = Information



Attempts at exorcizing
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 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
“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


Ek

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
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


Sequence d is

highly informative

Sequence d is

complex


Bennett s measure of complexity
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
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 state1
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 state2
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


Direct Path

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

Ti!f (???)

Initial state unknown

For each transformation

only one initial state transforms

to final state

Hilbert Space

Initial state

Final state


Direct Path: Probabilistic

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

Ti!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/Ni=e-S(i)¿ 1

Initial state

Final state


Direct Path: Deterministic

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

Ti!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


Direct Path: Information

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

Ti!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


Ski-lift Path

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


Ski-lift Path

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

Torder!f

Ends with the specific, final state

Probability of success: P2=1

Energy cost: E2=

Initial state

Final state


Ski-lift Path: Information

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


Comparison between paths

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 paths

Ski-lift uses ordered-state and environmental information

to obtain controllability and reproducibility


How does complexity emerge and how is it maintained
How does Complexity Emerge?And How is it Maintained?

Disorder

Order

Information/Complexity


Bennett s measure of complexity1
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
Biological examples

  • Cell formation

  • Apoptosis

  • Embryonic development

  • Ecological development


The morphotropic state as the cellular progenitor of complexity
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 Complexitythe Ecological Progenitor of Complexity

Maintaining the complexity of civilization necessitates

huge reservoirs of order


Schr dinger s what is life revisited
Schrödinger’s “ ComplexityWhat is life?” revisited

Hilbert Space

Requires energy

High entropy

High information

High order

Redundancy

High complexity

(specific environment)

Requires information


BIBLIOGRAPHY Complexity

  • 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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