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Maxwell's Demon: Implications for Evolution and Biogenesis

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

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  1. Maxwell's Demon: Implications for Evolution and Biogenesis Avshalom C. ElitzurIyar, The Israeli Institute for Advanced Research Copyleft 2010

  2. The Relevance of Thermodynamicsto Life Sciences • Thermodynamics is a discipline that studies energy, entropy, and information

  3. 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:

  4. 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:

  5. 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

  6. Whence the entropy differencebetween animate and inanimate systems ? The Common Textbook Answer: “Living organisms are open systems” ?

  7. Open Systems: Rocks Chairs Blackboards Trash cans (!) etc.

  8. The Thesis: Adaptation = Information

  9. Maxwell’s Demon

  10. Attempts at Exorcizing • Kelvin: The devil is alive • Von Smoluchowski: It’s intelligent • Szilard, Brillouin: It uses information • Bennett & Landauer: It erases information

  11. 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

  12. “Less energy, at the right time/place”

  13. “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

  14. 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

  15. 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

  16. 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

  17. Sequence d is highly informative Sequence d is complex

  18. 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

  19. The Ski-Lift Pathway: Thermodynamically Unique, Biologically UbiquitousGoren Gordon & Avshalom C. Elitzur High Order Requires Energy Spontaneous Low Order

  20. 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

  21. 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

  22. 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

  23. 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.

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. How does Complexity Emerge?And How is it Maintained? Disorder Order Information/Complexity

  34. 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

  35. Biological examples • Cell formation • Apoptosis • Embryonic development • Ecological development

  36. 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.

  37. Order as the Ecological Progenitor of Complexity Maintaining the complexity of civilization necessitates huge reservoirs of order

  38. Schrödinger’s “What is life?” revisited Hilbert Space Requires energy High entropy High information High order Redundancy High complexity (specific environment) Requires information

  39. BIBLIOGRAPHY • 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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