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Information Engines: Controlling Energy Flows and Efficient Energy Storage in Nano Devices

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

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Information Engines: Controlling Energy Flows and Efficient Energy Storage in Nano Devices

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  1. 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.how-why.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)

  2. 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 transmitter wall outlet receiver Energy ← Information ← Energy Information Engine Computer

  3. 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

  4. History of Information Engines • Maxwell’s Demon (J.C. Maxwell, A Theory of Heat, 1871) (1) Use initial position to sort with door (2) Lock the door Demon Demon (4) Reinsert wall with door (3) wall pressure x distance = energy Demon Demon

  5. 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

  6. 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

  7. 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.

  8. 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 K0is 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

  9. 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

  10. 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?

  11. 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 ynmost likely state snwidth 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, PRL96, 044101-1-4 (2006). http://server10.how-why.com/papers/strelioff05.pdf

  12. 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).

  13. 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

  14. 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

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