Thermodynamics of computing with circuits

Digital computers implement computations using circuits, as do many naturally occurring systems (e.g., gene regulatory networks). The topology of any such circuit restricts which variables may be physically coupled during the operation of a circuit. We investigate how such restrictions on the physical coupling affects the thermodynamic costs of running the circuit. To do this we first calculate the minimal additional entropy production that arises when we run a given gate in a circuit. We then build on this calculation, to analyze how the thermodynamic costs of implementing a computation with a full circuit, comprising multiple connected gates, depends on the topology of that circuit. This analysis provides a rich new set of optimization problems that must be addressed by any designer of a circuit, if they wish to minimize thermodynamic costs.

[1]  Artemy Kolchinsky,et al.  Exact, complete expressions for the thermodynamic costs of circuits , 2018, ArXiv.

[2]  Lulu Qian,et al.  Supporting Online Material Materials and Methods Figs. S1 to S6 Tables S1 to S4 References and Notes Scaling up Digital Circuit Computation with Dna Strand Displacement Cascades , 2022 .

[3]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[4]  Sosuke Ito,et al.  Information thermodynamics on causal networks. , 2013, Physical review letters.

[5]  Neil Gershenfeld,et al.  Signal Entropy and the Thermodynamics of Computation , 1996, IBM Syst. J..

[6]  A. B. Boyd,et al.  Identifying functional thermodynamics in autonomous Maxwellian ratchets , 2015, 1507.01537.

[7]  Robert Wille,et al.  Reversible Circuits: Recent Accomplishments and Future Challenges for an Emerging Technology - (Invited Paper) , 2012, VDAT.

[8]  F. Schlögl,et al.  On stability of steady states , 1971 .

[9]  Christopher Jarzynski,et al.  Work and information processing in a solvable model of Maxwell’s demon , 2012, Proceedings of the National Academy of Sciences.

[10]  James P. Crutchfield,et al.  Above and Beyond the Landauer Bound: Thermodynamics of Modularity , 2017, Physical Review X.

[11]  Dean J. Driebe,et al.  Generalization of the second law for a transition between nonequilibrium states , 2010 .

[12]  D. Wolpert,et al.  Dependence of dissipation on the initial distribution over states , 2016, 1607.00956.

[13]  H. Hasegawa,et al.  Generalization of the Second Law for a Nonequilibrium Initial State , 2009, 0907.1569.

[14]  Michael P. Frank,et al.  Introduction to reversible computing: motivation, progress, and challenges , 2005, CF '05.

[15]  M. Esposito,et al.  Three faces of the second law. I. Master equation formulation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Christopher A. Voigt,et al.  Principles of genetic circuit design , 2014, Nature Methods.

[17]  David H. Wolpert,et al.  Extending Landauer's Bound from Bit Erasure to Arbitrary Computation , 2015, 1508.05319.

[18]  J. Cheverud,et al.  Modularity: genes, development and evolution. , 2016, Annual review of ecology, evolution, and systematics.

[19]  S Turgut.  Relations between entropies produced in nondeterministic thermodynamic processes. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Hod Lipson,et al.  The evolutionary origins of modularity , 2012, Proceedings of the Royal Society B: Biological Sciences.

[21]  David H. Wolpert,et al.  The Free Energy Requirements of Biological Organisms; Implications for Evolution , 2016, Entropy.

[22]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[23]  Paul M. Riechers,et al.  Transforming Metastable Memories: The Nonequilibrium Thermodynamics of Computation , 2018, The Energetics of Computing in Life and Machines.

[24]  David H. Wolpert,et al.  The stochastic thermodynamics of computation , 2019, Journal of Physics A: Mathematical and Theoretical.

[25]  Nicole Yunger Halpern,et al.  The resource theory of informational nonequilibrium in thermodynamics , 2013, 1309.6586.

[26]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[27]  Joshua A. Grochow,et al.  Beyond Number of Bit Erasures: New Complexity Questions Raisedby Recently discovered thermodynamic costs of computation , 2018, SIGA.

[28]  M. Deem.  Statistical Mechanics of Modularity and Horizontal Gene Transfer , 2013 .

[29]  Gernot Schaller,et al.  Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions , 2016, 1610.01829.

[30]  Roberto Bruni,et al.  Models of Computation , 2017, Texts in Theoretical Computer Science. An EATCS Series.

[31]  T. Sagawa,et al.  Information Flow and Entropy Production on Bayesian Networks , 2015, 1506.08519.

[32]  H. Shaffer,et al.  Annual review of ecology, evolution, and systematics , 2003 .

[33]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .

[34]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[35]  Michael Satosi Watanabe,et al.  Information Theoretical Analysis of Multivariate Correlation , 1960, IBM J. Res. Dev..

[36]  Jonathan M. Borwein,et al.  Notions of Relative Interior in Banach Spaces , 2003 .

[37]  Søren Johansen,et al.  The Imbedding Problem for Finite Markov Chains , 1973 .

[38]  Linda C. van der Gaag,et al.  Probabilistic Graphical Models , 2014, Lecture Notes in Computer Science.

[39]  T. Rogers,et al.  From empirical data to time-inhomogeneous continuous Markov processes. , 2016, Physical review. E.

[40]  S. Lloyd.  Ultimate physical limits to computation , 1999, Nature.

[41]  Massimiliano Esposito,et al.  Ensemble and trajectory thermodynamics: A brief introduction , 2014, 1403.1777.

[42]  Masahito Ueda,et al.  Second law of thermodynamics with discrete quantum feedback control. , 2007, Physical review letters.

[43]  伊藤 創祐.  Information thermodynamics on causal networks and its application to biochemical signal transduction , 2015 .

[44]  A. Caticha.  Information and Entropy , 2007, 0710.1068.

[45]  R. Renner,et al.  The minimal work cost of information processing , 2012, Nature Communications.

[46]  Takahiro Sagawa,et al.  Information-thermodynamic characterization of stochastic Boolean networks , 2018, 1803.04217.

[47]  Lloyd.  Use of mutual information to decrease entropy: Implications for the second law of thermodynamics. , 1989, Physical review. A, General physics.

[48]  Massimiliano Esposito,et al.  Detailed Fluctuation Theorems: A Unifying Perspective , 2018, Entropy.

[49]  Ingo Wegener,et al.  The complexity of Boolean functions , 1987 .

[50]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[51]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[52]  Artemy Kolchinsky,et al.  A space–time tradeoff for implementing a function with master equation dynamics , 2019, Nature Communications.

[53]  Massimiliano Esposito,et al.  Finite-time thermodynamics for a single-level quantum dot , 2009, 0909.3618.

[54]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[55]  U. Seifert.  Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[56]  Massimiliano Esposito,et al.  Second law and Landauer principle far from equilibrium , 2011, 1104.5165.

[57]  R. Weiss,et al.  Directed evolution of a genetic circuit , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[58]  O. Maroney.  Generalizing Landauer's principle. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  F. Brandão,et al.  Resource theory of quantum states out of thermal equilibrium. , 2011, Physical review letters.

[60]  Rui-Sheng Wang,et al.  Boolean modeling in systems biology: an overview of methodology and applications , 2012, Physical biology.

[61]  Kalyan S. Perumalla,et al.  Introduction to Reversible Computing , 2013 .

[62]  J. Schnakenberg.  Network theory of microscopic and macroscopic behavior of master equation systems , 1976 .

[63]  G. Crooks.  Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems , 1998 .

[64]  David H. Wolpert,et al.  Number of hidden states needed to physically implement a given conditional distribution , 2017, New Journal of Physics.

[65]  T. Sagawa.  Thermodynamic and logical reversibilities revisited , 2013, 1311.1886.

[66]  M. N. Bera,et al.  Thermodynamics from Information , 2018, 1805.10282.

[67]  Masahito Ueda,et al.  Fluctuation theorem with information exchange: role of correlations in stochastic thermodynamics. , 2012, Physical review letters.