Demon Dynamics: Deterministic Chaos, the Szilard Map, & the Intelligence of Thermodynamic Systems.


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1 Demon Dynamics: Deterministic Chaos, the Szilard Map, & the Intelligence of Thermodynamic Systems Jim Crutchfield Complexity Sciences Center Physics Department University of California at Davis Information Engines Telluride Science Research Center Telluride, Colorado 23 June 26
2 bstract We introduce a deterministic chaotic system the Szilard Map that encapsulates the measurement, control, and erasure protocol by which Maxwellian Demons extract work from a heat reservoir. Implementing the Demon's control function in a dynamical embodiment, our construction symmetrizes Demon and thermodynamic system, allowing one to explore their functionality and recover the fundamental tradeoff between the thermodynamic costs of dissipation due to measurement and due to erasure. The map's degree of chaos captured by the KolmogorovSinai entropy is the rate of energy extraction from the heat bath. Moreover, an engine's statistical complexity quantifies the minimum necessary system memory for it to function. In this way, dynamical instability in the control protocol plays an essential and constructive role in intelligent thermodynamic systems. Joint work with lexander B. Boyd.
3 History of Computing Substrates nalog: Mechanical gears nalog: Electron tube circuits Digital Gates: Electron tubes, semiconductors Digital Memory: Mercury delay lines, storage scopes,... Molecular Computing (97s) Physics & Computation (MIT Endicott House 98) Quantum Computing: Feynman Erasure cost: Bennett & Landauer It from Bit: Wheeler Josephson Junction Computers (IBM 98s) Nanotech (Drexler/Merkle XEROX PRC 99s) Design goal: Useful computing
4 History Of Intrinsic Computing Nature already computes Information: H(Pr(X)) (Shannon 94s) h µ In chaotic dynamics: (Kolmogorov 95s) Physics & Computation (MIT Endicott House 98) Intrinsic computing there too!
5 Industrial Revolution 75s9 Humans commandeer energy on vast scales. Unprecedented improvement in human condition.
6 Industrial Revolution 75s9 Urbanization, disease,... Class inequality & oppression
7 genda intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
8 genda Structure! intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
9 Structure!
10 Biological Structure In what ways does nature organize? (Phenomenology) How does it organize? (Mechanism) re these levels real or merely convenient? (Objectivity) Why does nature organize? (Optimization versus chance versus...) Physics Today, March 26
11 Foundations: Computational Mechanics B Environment C C µ =... Sensory Data Pr(s ) 3 gent Model εmachine: Unique, minimal, & optimal predictor X 2S Causal Equivalence: x x, Pr(! X x )=Pr(! X x ) B 2/3 /3 Stored versus Generated Information Pr( ) log 2 Pr( ) versus h µ = X 2S /2 /2 Pr( ) X 2S Pr( ) log 2 Pr( ) C
12 Foundations: Computational Mechanics B Environment C C µ =... Sensory Data Pr(s ) 3 gent Model εmachine: Unique, minimal, & optimal predictor X 2S Causal Equivalence: x x, Pr(! X x )=Pr(! X x ) Structure versus Randomness B 2/3 /3 Stored versus Generated Information Pr( ) log 2 Pr( ) versus h µ = X 2S /2 /2 Pr( ) X 2S Pr( ) log 2 Pr( ) C
13 Foundations: Computational Mechanics B Environment C C µ =... Sensory Data Pr(s ) 3 gent Model εmachine: Unique, minimal, & optimal predictor X 2S Causal Equivalence: x x, Pr(! X x )=Pr(! X x ) B 2/3 /3 Stored versus Generated Information Pr( ) log 2 Pr( ) versus h µ = X 2S /2 /2 Pr( ) X 2S Pr( ) log 2 Pr( ) C Intrinsic Computation:. How much historical information does a process store? 2. In what architecture is it stored? 3. How is it used to produce future behavior? J.P. Crutchfield & K. Young, Inferring Statistical Complexity, Physical Review Letters 63 (989) 58. J.P. Crutchfield, Between Order and Chaos, Nature Physics 8 (January 22) 724.
14 Problem Statement = Ecological population dynamics of structurally complex adapting agents + Reproduction (evolutionary population dynamics) JP Crutchfield, The Calculi of Emergence: Computation, Dynamics, and Induction, Physica D 75 (994) 54. In Proceedings of the Oji International Seminar: Complex Systems from Complex Dynamics to rtificial Reality 59 pril 993, Numazu, Japan.
15 genda intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
16 Maxwell s Demon James Clerk & Katherine Maxwell (865)... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us.... Now let us suppose that... a vessel is divided into two portions, and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from to B, and only the slower molecules to pass from B to. He will thus, without expenditure of work, raise the temperature of B and lower that of, in contradiction to the second law of thermodynamics....
17 Maxwell s Demon Demon creates order out of chaos.
18 Maxwell s Demon Demon creates order out of chaos.
19 Maxwell s Demon Demon creates order out of chaos. Uses molecular information to convert heat to temperature difference & so to useful work.
20 genda intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
21 Szilard s Engine: ON THE DECRESE OF ENTROPY IN THERMODYNMIC SYSTEM BY THE INTERVENTION OF INTELLIGENT BEINGS, Leo Szilard, Zeitschrift fur Physik 65 (929) we must conclude that the intervention which establishes the coupling between y and x, the measurement of x by y, must be accompanied by a production of entropy.
22 Szilard s SingleMolecule Engine Cycle Reset State ) Single Particle Left: Right: B Demon Insert Barrier 2) Demon Observes 3) B Measure Work Extraction 4) B Control Remove Barrier 5) B Reset 6) Erase
23 Szilard s Engine: ON THE DECRESE OF ENTROPY IN THERMODYNMIC SYSTEM BY THE INTERVENTION OF INTELLIGENT BEINGS, Leo Szilard, Zeitschrift fur Physik 65 (929) a simple inanimate device can achieve the same essential result as would be achieved by the intervention of intelligent beings. We have examined the biological phenomena of a nonliving device and have seen that it generates exactly that quantity of entropy which is required by thermodynamics.
24 ... a Chaotic Dynamical System lec Boyd and JPC, Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems, Physical Review Letters 6 (26) 96. arxiv.org: [condmat.statmech]. SUS B SUS B Measure Demon T Measure Demon L R L R SUS B SUS B Extract Energy from Heat Bath Demon T Control Demon L R L R SUS B SUS B Erase Demon Memory Demon T Erase Demon L R L R
25 ... a Chaotic Dynamical System lec Boyd and JPC, Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems, Physical Review Letters 6 (26) 96. arxiv.org: [condmat.statmech]. SUS B SUS B SUS B SUS B Demon T Measure Demon T Control Demon T Erase Demon L R L R L R L R
26 The Szilard Map Measure Control Erase T M (x, y) = T C (x, y) = T E (x, y) = 8 (x, y) >< x<,y < or x<,y, x, + y x,y apple, >: x, x,y >. y ( ( x,y) x<, x. x,y ( (x, y ) y<, x, + y ( ) y. T Szilard (x, y) =T E (x, y) T C (x, y) T M (x, y)
27
28
29 The Szilard Map: Controller Symbolic Dynamics Machine: Minimal Optimal Generator in = {M,C,E} a 3 L M : b 3 RB M : Demon Memory Molecule Position out = {, B} {L, R} L E : R E : c d e L C : RB C : LB C : R C : f 3 Entropy Rate: h µ = H( )bits Statistical Complexity: C µ = H[Pr( )] = log H( )bits
30 genda intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
31 The Szilard Engine: Thermodynamical System Dynamics Thermodynamics T M (x, y) Measure Qmeasure = k B T ( )ln(( )/ ) T C (x, y) Control Qcontrol = kb T H( )ln2 Qerase = T E (x, y) Erase k B T ( )ln(( )/ ) + k B T H( )ln2
32 Energy Dissipation: Erasure and Measurement! Q diss (kt) 3 2 = b Erasure:! Measurement:! Feedback: Control:
33 Energy Dissipation: Erasure and Measurement! Q diss 3 2 (kt) Landauer Principle = b Erasure:! Measurement:! Feedback: Control:
34 Energy Dissipation: Erasure and Measurement! Q diss (kt) Landauer nti Landauer 3 Principle Principle 2 = b Erasure:! Measurement:! Feedback: Control:
35 Information Engines: n nalytical Strategy (i) n information engine is the dynamic over a joint state space of a thermodynamic system and a physically embodied controller. (ii) The causal states of the joint dynamics, formed from the predictive equivalence classes of system histories, capture its information processing and emergent organization. (iii) necessary component of the engine s effective intelligence, its memory, is given by its statistical complexity. (iv) Its dissipation is given by the dynamical system negative LCEs, and (v) the rate of energy extracted from the heat bath is governed by the KolmogorovSinai entropy. h µ C µ
36 genda intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
37 Information Ratchets Net Work Extraction! Z N X N Thermal Reservoir Q W Mass output string Ratchet input string. Y :N Output h µ Information Reservoir Y N: h µ Input. Boyd, D. Mandal, and JPC, Identifying Functional Thermodynamics in utonomous Maxwellian Ratchets. New Journal of Physics 8 (26) arxiv.org: [condmat.statmech]
38 Information Ratchets Second Law for Intrinsic Computation hw i kb T ln 2 hµ hµ Eraser. Eraser q H Dud p Engine..5 p Engine. Entropy Rates H() = H () H() hµ = hµ hµ Eraser Eraser q Thermodynamic Functions
39 ENERGY HRVESTING GENTS (Paul Riechers and JPC, Structural Thermodynamics of daptation, In prep. : 2 : 2 : 2 + : 2 + : + : + 2 : 3 2 : 4 : : : 2 : + 2 : + L R L gent R : 2 : : Optimal agent Suboptimal agent Stochastic environment Must sync to environment
40 ENERGY HRVESTING GENTS (Paul Riechers and JPC, Structural Thermodynamics of daptation (26).) : 2 : 2 : 2 + : 2 + : + : + 2 : 3 2 : 4 : : : 2 : + 2 : + L R : 2 : : Optimal agent Suboptimal agent Stochastic environment Must sync to environment
41 ENERGY HRVESTING GENTS (Paul Riechers and JPC, Structural Thermodynamics of daptation (26).) : 2 : 2 : 2 + : 2 + : + : + 2 : 3 2 : 4 : : : 2 : + 2 : + L R : 2 : : Optimal agent Suboptimal agent Stochastic environment Must sync to environment
42 genda intrinsic computation Maxwell s Demon Szilard s Engine Thermodynamical Systems pplications: Ratchets, daptation Intelligence?
43 Intelligence? Maxwells Demon: n intelligent being?
44 Laplace s Demon The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence which at a given instant comprehends all the relations of the entities of this universe, it could state the respective positions, motions, and general affects of all these entities at any time in the past or future. Pierre Simon de Laplace (776)
45 Thanks! B. Boyd and J. P. Crutchfield, Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems, Physical Review Letters 6 (26) 96. arxiv.org: [condmat.statmech]. B. Boyd, D. Mandal, and J. P. Crutchfield, Identifying Functional Thermodynamics in utonomous Maxwellian Ratchets, New Journal of Physics 8 (26) arxiv.org: [condmat.statmech] Paul Riechers and J. P. Crutchfield, Structural Thermodynamics of daptation (26) in preparation.
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