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
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
I 0
With information reducing the possible states to P1:
P0
I  K ln
 K (ln P0  ln P1 )
P1
Ideally, for P1=1:
I  K ln P0
Shannon’s Information:
Uncertainty = Entropy
Boltzmann’s Entropy
For all states being equiprobable:
S  k ln W
Otherwise:
w
S  k  p1 ln p1
j i
27
Information of one English letter:
i  k  p1 ln p1
j 1
For a string of G letters:
jm
I  G  i  Gk  p1 ln p1
j i
The Relevance of Thermodynamics
to 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 difference
between 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.
2.
3.
4.
Kelvin: The devil is alive
Von Smoluchowski: It’s intelligent
Szilard, Brillouin: It uses information
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) molecules
reach the synapses with enormous
precision
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
Ek
Et
Ec
Ee
Et
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, Complex
Measures 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.
3333333333333333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333
1860271194945955774038867706591873856869843786230090655440
136901425331081581505348840600451256617983
0123456789012345678901234567890123456789012345678901234567
890123456789012345678901234567890123456789
6180339887498948482045868343656381177203091798057628621354
486227052604628189024497072072041893911374
b.
c.
d.
5 1

2
Sequence d is
Sequence d is
highly informative
complex
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
High order
Low order
The Ski-Lift Pathway:
Thermodynamically Unique, Biologically Ubiquitous
Goren Gordon & Avshalom C. Elitzur
High Order
Requires
Energy
Spontaneous
Low Order
How do you get to some desired state?
High Order
Requires
Energy
Spontaneous
Initial State
Low Order
Desired State
Step 1:
Use Ski-Lift,
get to the
top
How do you get to some desired state?
High Order
Requires
Energy
Spontaneous
Initial State
Low Order
Desired State
Step 1:
Use Ski-Lift,
get to the
top
How do you get to some desired state?
High Order
Requires
Energy
Spontaneous
Step 1:
Use Ski-Lift,
get to the
top
Step 2:
Ski down
Initial State
Low Order
Desired State
The Ski-Lift Conjecture (Gordon & Elitzur, 2009):
Life approaches complexity “from above,” i.e., from the highorder 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. Probabilistic
2. Deterministic
Entropy
1. Direct path
Ski-lift
2. Ski-lift theorem
Initial state
Direct path
Final state
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
Final state
Initial 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
Final state
Energy cost:
E=
Probability of success:
P=1/Ni=e-S(i)¿ 1
Initial 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
Repeat transformation until final
state is reached
Probability of success:
P=1
Average energy cost:
E= eS(i)À 1
Hilbert Space
Final state
Initial 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)
Hilbert Space
Then can perform the
right transformation once
Probability of success:
P=1
Energy cost:
E=
Information required:
I=S(i)+S(f)
Final state
Initial 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
Final state
Initial 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)
Stage 2: Controlled transformation
Torder!f
Ends with the specific, final state
Probability of success: P2=1
Energy cost: E2=
Hilbert Space
Final state
Initial 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
Final state
Initial state
Comparison between paths
Direct Path
1. Probabilistic
1. Low probability
2. Low energy
2. Deterministic:
1. High probability
2. High energy
3. Information:
•
•
•
•
•
Ski-lift
Deterministic
Controlled
Reproducible
Costs low energy
Requires only
environmental information
1. Requires much information
2. Low energy
Ski-lift uses ordered-state and environmental information
to obtain controllability and reproducibility
How does Complexity Emerge?
And How is it Maintained?
Order
Information/Complexity
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?
complexity
High order
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,
Nat. Rev. Mol. Cell Biol. Jan;3(1):50-60.
order and survival.”
Maintaining the complexity of civilization necessitates
huge reservoirs of order
Schrödinger’s “What is life?” revisited
Hilbert Space
Requires
energy
High order
Redundancy
High complexity
(specific environment)
Requires
information
High entropy
High 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