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The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous

The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous Goren Gordon Weizmann Institute of Science Rehovot Avshalom C. Elitzur www.a-c-elitzur.co.il. Outline. The Goal: A Unified Physical Set of Principles Underlying all Forms of Life Entropy, Information and Complexity

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The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous

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  1. The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous Goren GordonWeizmann Institute of ScienceRehovot Avshalom C. Elitzur www.a-c-elitzur.co.il

  2. Outline • The Goal: A Unified Physical Set of Principles Underlying all Forms of Life • Entropy, Information and Complexity • The new Question: How do Transitions from High-to-High-Entropy States Take Place? • The Ski-Lift Model

  3. 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 • 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 • 6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374

  4. Sequence d is highly informative Sequence d is complex

  5. Bennett’s Measure of Complexity Given A sequence’s shortest algorithm, how much computation is needed to produce it from the algorithm, or conversely to compress it back into it?

  6. Complexity is not directly related to Order/Entropy complexity Low order High order

  7. Ordered, Random, Alive

  8. Maxwell’s Demon

  9. A Lawful Maxwell’s Demon in a Complex Environment

  10. A Lawful Maxwell’s Demon in a Complex Environment

  11. Interim Summary Thermodynamics offers a ubiquitous physical basis for the understanding of numerous biological phenomena, through the introduction of concepts like entropy/order, information and complexity.

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

  13. The Hypothesis: Ski-Lift High Order Requires Energy Spontaneous Low Order

  14. The Hypothesis: Ski-Lift High Order Step 1: Use Ski-Lift, get to the top Requires Energy Spontaneous X Desired state Low Order

  15. The Hypothesis: Ski-Lift High Order Step 1: Use Ski-Lift, get to the top Requires Energy Spontaneous Step 2: Ski down X Desired state Low Order

  16. The Ski-Lift Conjecture: 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.

  17. Dynamical evolution of complex states How to reach a complex state? Initial state at equilibrium (unknown, high entropy) Final complex state, defined by environment • Direct path • Probabilistic • Deterministic • Ski-lift theorem Ski-lift Entropy Final state Initial state Direct path

  18. Definitions – state N – equivalent microstates of  Entropy of state: S()=log(N) Initial state, i – high entropy,NiÀ 1 Final state, f – high complexity, specific, S(f)=S(i) • Operations allowed: • S-: Decrease entropy. • Uncontrolled • Energy cost: E=S • 2. T: Transformation. • Controlled, requires information • Does not change entropy on average, <S(T) – S()>=0 • Energy cost: E=

  19. Numerical example =a0a1a2….an i=18602711949459557740 (or any other random number) f=61803398874989484820 (a specific, complex number) order=00000000000000000000 18602711949459557740 • Operations: • S-: Decrease entropy. • Uncontrolled. E= S 10602001040050500740 E= S 00000000000000000000

  20. Numerical example =a0a1a2….an i=18602711949459557740 (or any other random number) f=61803398874989484820 (a specific, complex number) order=00000000000000000000 • Operations: • S-: Decrease entropy. • Uncontrolled • 2. T: Transformations. • Addition. • <S(T)-S()>=0 • due to symmetry T1=(+4)(+2)(+0)(+6)….(+1) T2=(+1)(+7)(+8)(+3)….(+9) … T1I =50662711949459557741 T2order=17830000000000000009

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

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

  30. Biological examples • Cell formation • Embryonic development • Natural selection • Ecological development

  31. Cell formation Initial state: free molecules in primordial pool Ski-lift model 1. Increased order: compartmentalization 2. Controlled transformation: specialization Direct path Improbable, Irreproducible

  32. Embryonic development Initial state: fertilized ovum + nutrients Ski-lift model 1. Increased order: mitosis, Blastocyte 2. Controlled transformation: differentiation Direct path Differentiation to final organism Improbable, irreproducible due to high susceptibility to environmental variations

  33. The Morphotropic State as the Embryonic Progenitor of Complexity

  34. 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.

  35. Natural selection Initial state: Individual + resources Ski-lift model 1. Increased order: reproduction 2. Controlled transformation: minor mutations Direct path Large mutations. Attempts to reach “optimized” organism at “one go”. Improbable, irreproducible due to high susceptibility to environmental variations

  36. Ecological development Initial state: Natural complexity Ski-lift model 1. Increased order: accumulate resources 2. Controlled transformation: build cities Direct path Develop technology without a controlled environment

  37. The Morphotropic State as the Ecological Progenitor of Complexity

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