The Ski-Lift Pathway: Thermodynamically Unique,

Biologically Ubiquitous

Goren GordonWeizmann Institute of Science

Rehovot

Avshalom C. Elitzurwww.a-c-elitzur.co.il

Outline

1. The Goal: A Unified Physical Set of Principles Underlying all Forms of Life

2. Entropy, Information and Complexity3. The new Question: How do Transitions from High-

to-High-Entropy States Take Place?4. The Ski-Lift Model

Ordered, Random, ComplexMeasures of Orderliness

1. Divergence from equiprobability (Gatlin)

(Are there any digits in the sequence that are more common?)

2. Divergence from independence (Gatlin)

(Is there any dependence between the digits?)

3. Redundancy (Chaitin)

(Can the sequence be compressed into any shorter algorithm?)

a. 3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333

b. 1860271194945955774038867706591873856869843786230090655440136901425331081581505348840600451256617983

c. 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

d. 6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374

2

15

Sequence d is complex

Sequence d is highly informative

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?

Complexity is not directly related to Order/Entropy

High order

complexity

Low order

Ordered, Random, Alive

Maxwell’s Demon

A Lawful Maxwell’s Demon in a Complex Environment

A Lawful Maxwell’s Demon in a Complex Environment

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.

How does Complexity Emerge?And How is it Maintained?

Order Information/Complexity Disorder

The Hypothesis: Ski-Lift

High Order

Low Order

RequiresEnergy

Spontaneous

X Desired state

High Order

Low Order

RequiresEnergy

Spontaneous

The Hypothesis: Ski-Lift

Step 1:Use Ski-

Lift, get to the top

X Desired state

High Order

Low Order

RequiresEnergy

Spontaneous

The Hypothesis: Ski-Lift

Step 2:Ski down

Step 1:Use Ski-

Lift, get to the top

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.

Dynamical evolution of complex states

How to reach a complex state?

Initial state at equilibrium (unknown, high entropy)

Final complex state, defined by environment

1. Direct path

1. Probabilistic

2. Deterministic

2. Ski-lift theorem

Initial state Final state

Ent

ropy

Direct path

Ski-lift

Definitions

– stateN – equivalent microstates of Entropy of state: S()=log(N)

Initial state, i – high entropy,Ni À 1

Final state, f – high complexity, specific, S(f)=S(i)

Operations allowed:

1. S-: Decrease entropy.1. Uncontrolled2. Energy cost: E=S

2. T: Transformation.• Controlled, requires information• Does not change entropy on average, <S(T) – S()>=0• Energy cost: E=

Numerical example=a0a1a2….an

i=18602711949459557740 (or any other random number)

f=61803398874989484820 (a specific, complex number)

order=00000000000000000000

Operations:1. S-: Decrease entropy.

Uncontrolled.

18602711949459557740

10602001040050500740

00000000000000000000

E= S

E= S

Numerical example=a0a1a2….an

i=18602711949459557740 (or any other random number)

f=61803398874989484820 (a specific, complex number)

order=00000000000000000000

Operations:1. S-: Decrease entropy.

Uncontrolled

2. T: Transformations.Addition.<S(T)-S()>=0due to symmetry

T1=(+4)(+2)(+0)(+6)….(+1)T2=(+1)(+7)(+8)(+3)….(+9)…

T1I =50662711949459557741 T2order=17830000000000000009

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 stateFinal 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

Perform transformation once

Energy cost:E=

Probability of success:P=1/Ni

=e-S(i)¿ 1

Hilbert Space

Initial stateFinal state

Direct Path: Probabilistic

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

Repeat transformation until finalstate is reached

Probability of success:P=1

Average energy cost:E= eS(i)À 1

Direct Path: Deterministic

Hilbert Space

Initial stateFinal state

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

Ti!f

If one has information about initial stateIi=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)

Direct Path: Information

Hilbert Space

Initial stateFinal state

Two stages path:

Stage 1: Increase orderS-i! order

Ends with a specific, known stateProbability of success: P1=1Energy cost: E1=S(i)

Ski-lift Path:

Hilbert Space

Initial stateFinal state

Two stages path:

Stage 1: Increase orderS-i! order

Ends with a specific, known stateProbability of success: P1=1Energy cost: E1=S(i)

Stage 2: Controlled transformationTorder!f

Ends with the specific, final stateProbability of success: P2=1Energy cost: E2=

Ski-lift Path:

Hilbert Space

Initial stateFinal 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 stateFinal state

Ski-lift Path: Information

Comparison between paths

Direct Path

1. Probabilistic1. Low probability

2. Low energy

2. Deterministic:1. High probability

2. High energy

3. Information:1. Requires much information

2. Low energy

Ski-lift• Deterministic• Controlled• Reproducible• Costs low energy• Requires only

environmental information

Ski-lift uses ordered-state and environmental information to obtain controllability and reproducibility

“What is life?” revisitedHilbert Space

High orderRedundancy

High entropyHigh informationHigh complexity

(specific environment)

Requires energy

Requires information

Biological examples

• Cell formation

• Embryonic development

• Natural selection

• Ecological development

Cell formation

Initial state: free molecules in primordial pool

Ski-lift model

1. Increased order: compartmentalization

2. Controlled transformation: specialization

Direct path

Improbable, Irreproducible

Embryonic development

Initial state: fertilized ovum + nutrientsSki-lift model1. Increased order: mitosis, Blastocyte 2. Controlled transformation: differentiation

Direct pathDifferentiation to final organismImprobable, irreproducible due to highsusceptibility to environmental variations

The Morphotropic State as the Embryonic 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.

Natural selection

Initial state: Individual + resourcesSki-lift model1. Increased order: reproduction 2. Controlled transformation: minor mutations

Direct pathLarge mutations. Attempts to reach “optimized”

organism at “one go”.Improbable, irreproducible due to highsusceptibility to environmental variations

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

The Morphotropic State as the Ecological Progenitor of

Complexity