Download Information Engines Converting Information into Energy

Information Engines:
Controlling Energy Flows and Efficient
Energy Storage in Nano Devices
Alfred W. Hubler
Center for Complex Systems Research, UIUC
- Design of Information Engines=> Limiting factor: Molecular Chaos
- Better Efficiency with Chaos Predictors and Nonlinear Resonances
- Applications: Novel Devices for Energy Storage and Energy Transport
Information → Energy → Information → Energy → Information → Energy →
Bradley Chase, Alfred Hübler, Inverse Energy-Uncertainty Relation for a Simple Information Engine, preprint 2007, http://server10.howwhy.com/papers/Chase05.pdf
F. Yamaguchi, K. Kawamura, A. Hubler, Sudden Drop of Dissipation in Field-Coupled Quantum Dot Resistors, Jpn. J. Appl. Phys. 34, L 105-108
(1995)
H.Higuraskh, A. Toriumi, f. Yamaguchi, K. Kawamura, A. Hubler, Correlation Tunnel Device, U. S. Patent # 5,679,961 (1997)
Energy transfer with low-power,
high-information electrical fields:
Simple example: use forecast of atmospheric pressure to charge battery
generator
large container
rotor in a pipe
comp. controlled valve
Two types of electro-magnetic waves:
(a) High power, low information rate
(micro waves, solar radiation
DC & AC power lines)
(b) Low power, high information rate
(wireless communication, radio)
battery
receiver
Energy
transmitter
wall outlet
←
Information
←
Energy
Information Engine
Computer
Related concept in the financial sector:
conversion of information into profit
“Information Engine” in the financial sector: financial tool
which uses information to improve its performance
Financial tool: buying and selling stocks and other financial
instruments to make money (or loose money).
Currently, “Information Engines” use information from
chaos predictors and data mining algorithms to improve
their efficiency
History of Information Engines
• Maxwell’s Demon (J.C. Maxwell, A Theory of Heat, 1871)
(1) Use initial position to sort with door
Demon
(4) Reinsert wall with door
Demon
(2) Lock the door
Demon
(3) wall pressure x distance = energy
Demon
History of Information Engines
• Entropy and irreversible computation – resetting the memory
of the demon (Szilard 1929, Bennet 1987)
• Non-equilibrium fluctuations can perform work (Millonas
1995; Jayannavar 1996; Doering, Horsthemke, Riordan 1994)
• Relationship between energy and gravitational entropy in
black holes (Bekenstein 1981)
• Quantum demon (Lloyd 1997)
• Efficient air conditioner (Weinberg 1982)
This study: Information loss due to molecular chaos
Information Engine: Particle Dynamics
Particle motion: constant
velocity
Wall reflection: normal comp.
of velocity switches sign
Large uncertainty in the initial direction:
Small uncertainty in the initial position and initial speed
Information Engine: Controller Dynamics
• Numerical simulation of particle motion for an ensemble of
initial conditions.
• Estimates the probability Pl(t) and Pr(t) of the left or right
particle hitting the partition wall.
• Keeps the partition wall open unless the right particle might
escape, which occurs if Pr(t) > 0.
Energy consumption of controller is ignored.
Information Engine: Observables
• Pc , probability that both particles are captured in the right box
• W = 0.375 K0 , extractable energy if particles are in right box
where K0 is the initial energy of the two particles
• Wc = Pc W expectation value of extracted energy
Fraction of energy extracted versus the inverse of the initial angular uncertainty
for an ideal gas in a rectangular container (no molecular chaos):
- - numerical simulation ----- theory
Large initial uncertainty: extractable energy ~ inverse of initial uncertainty
Information Engine with Molecular Chaos
Container wall curved with radius R = 25
Container wall curvature (1/R) variable
- Fraction
of extractable energy ~ inverse of initial uncertainty
- Proportionality constant M decreases for large curvature 1/R,
where (1/R) is a measure for the amount of molecular chaos
Energy extraction requires a certain amount of time
=>Molecular chaos reduces the amount of extractable energy
Information Engine: Thermodynamic Limit
0 initial phase space volume ~ product of initial uncertainties
f final phase space volume ~ size of container
Reversible process:
S = W / T and S = k ln 
S entropy
T temperature
k Boltzmann constant
 W = K0 (1 - 0 / f) ≈ K0 » Wp
- The efficiency of this information engine is significantly below the
theoretical limit.
- Similar information engines with more particles are far less efficient
due to molecular chaos.
• How can we improve the information engine?
Predicting chaos with ensemble predictors
• Distribution functions are multimodal
Dynamics of state xn:
xn+1 = f(xn)
Dynamics of most likely state:
yn+1 = f(yc) if yn-sn /2 < yc < yn+sn /2
yn+1 = f(yn) else
yn most likely state
sn width of distribution
sn+1 = |f’(yn)| sn
Histogram of the occurrences of states for a chaotic Roessler system.The most likely trajectory
(black circle) and the trajectory of the initial state (gray triangle) are also provided.
C. Strelioff, A. Hübler, Medium-Term Prediction of Chaos, PRL 96, 044101-1-4 (2006).
http://server10.how-why.com/papers/strelioff05.pdf
Resonant energy extraction - Optimal coupling
between model and the real system
• A nonlinear dynamical system reacts most sensitive to its own
dynamics
Dynamics: xn+1= f(xn, a) + Fn
Model: yn+1 = f(yn, b)
Optimal force: Fn+1 = Fn /f ‘(yn+1, b)
Response: R=(xN-yN)2
Response of a chaotic logistic map f=a xn (1 - xn),
a=3.6 and the model f = b yn (1-yn).
- Resonances: 100% energy transfer possible
G. Foster, A. Hubler, Robust and Efficient Interaction with Complex Systems, Man & Cybernetics, 2029(2003).
Efficient energy storage and energy flow controls:
Resonant energy transfer between coupled quantum dots
F. Yamaguchi, K. Kawamura, A. Hubler, Sudden Drop of Dissipation in Field-Coupled Quantum Dot
Resistors, Jpn. J. Appl. Phys. 34, L 105-108 (1995)
H.Higuraskh, A. Toriumi, f. Yamaguchi, K. Kawamura, A. Hubler, Correlation Tunnel Device,
U. S. Patent # 5,679,961 (1997) – very large electric fields due to Pauli’s exclusion principle
Information Engines
Converting Information into Energy
- Design of Information Engines: information can make an
energy extraction tool more efficient
- Improvement with Chaos Predictors and Nonlinear Resonances
- Applications:
Reaction Nets - catalysts
Regulatory Nets - resonances = match dynamics
Communication nets - coupled quantum dots
Power grid - chaotic power lines
Energy storage - quantum wells and quantum dots
Information → Energy → Information → Energy → Information → Energy →
Bradley Chase, Alfred Hübler, Inverse Energy-Uncertainty Relation for a Simple Information
Engine, preprint 2007, http://server10.how-why.com/papers/Chase05.pdf