maxwell's demon: implications for evolution and biogenesis avshalom c. elitzur iyar, the...
TRANSCRIPT
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
1. 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:
)ln(lnln 101
0 PPKP
PKI
0I
0ln PKI
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:
w
ij
ppkS 11 ln
27
111 ln
j
ppki
mj
ij
ppGkiGI 11 ln
WkS ln
The Relevance of Thermodynamicsto Life Sciences
1. Thermodynamics is a discipline that studies energy, entropy, and information
2. 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”
?
Open Systems:
Rocks
Chairs
Blackboards
Trash cans (!)
etc.
The Thesis:
Adaptation = Information
Maxwell’s Demon
Attempts at Exorcizing
1. Kelvin: The devil is alive
2. Von Smoluchowski: It’s intelligent
3. Szilard, Brillouin: It uses information
4. 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”
“Less energy, at the right time/place”:Comparison between two methods of kill
Considerable mechanical energy: Crushing the entire prey’s body
Minute chemical energy: Neurotoxin (cobrotoxin) moleculesreach the synapses with enormous precision
Ek Et
Ec EtEe
The Demon Vs. the Living Organism: The Analogy
1) Life increases energy’s efficiency, up the thermodynamic scale
2) It does that with the aid of information
Ec + Ee Ec'> Ec
Ec + Ee Ek
The Demon Vs. the Living Organism: The Disanalogy
1) The real environment is never completely disordered but complex
2) The organism does not create order but complexity
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. 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789
d. 6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374
2
15
Sequence d is complex
Sequence d is highly informative
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?
High order
complexity
Low order
The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous
Goren Gordon & Avshalom C. Elitzur
High Order
Low Order
RequiresEnergy
Spontaneous
Desired State
High Order
Low Order
RequiresEnergy
Spontaneous
Step 1:Use Ski-Lift,
get to the top
How do you get to some desired state?
Initial State
High Order
Low Order
RequiresEnergy
Spontaneous
Step 1:Use Ski-Lift,
get to the top
How do you get to some desired state?
Desired State Initial State
High Order
Low Order
RequiresEnergy
Spontaneous
Step 2:Ski down
Step 1:Use Ski-Lift,
get to the top
How do you get to some desired state?
Desired State Initial State
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?
1. Direct path
1. Probabilistic
2. Deterministic
2. Ski-lift theorem
Initial state Final state
Ent
ropy
Direct path
Ski-lift
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 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)
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
How does Complexity Emerge?And How is it Maintained?
Information/ComplexityOrder Disorder
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?
High order
complexity
Low 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 necessitateshuge reservoirs of order
Schrödinger’s “What is life?” revisited
Hilbert Space
High orderRedundancy
High entropyHigh informationHigh complexity
(specific environment)
Requires energy
Requires information
BIBLIOGRAPHY
1. Leff, H. S., & Rex, A. F. (2003) Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing. Bristol: Institute of Physics Publishing.
2. Dill, K.A. , & Bromberg, S. (2003) Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology. New York: Garland Science.
3. Di Cera, E., Ed. (2000) Thermodynamics in Biology” Oxford: Oxford University Press.
4. 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