Balancing Error and Dissipation in Computing

Modern digital electronics support remarkably reliable computing, especially given the challenge of controlling nanoscale logical components that interact in fluctuating environments. However, we demonstrate that the high-reliability limit is subject to a fundamental error-energy-efficiency tradeoff that arises from time-symmetric control: Requiring a low probability of error causes energy consumption to diverge as logarithm of the inverse error rate for nonreciprocal logical transitions. The reciprocity (self-invertibility) of a computation is a stricter condition for thermodynamic efficiency than logical reversibility (invertibility), the latter being the root of Landauer's work bound on erasing information. Beyond engineered computation, the results identify a generic error-dissipation tradeoff in steady-state transformations of genetic information carried out by biological organisms. The lesson is that computation under time-symmetric control cannot reach, and is often far above, the Landauer limit. In this way, time-asymmetry becomes a design principle for thermodynamically efficient computing.

[1]  C. Jarzynski.  Hamiltonian Derivation of a Detailed Fluctuation Theorem , 1999, cond-mat/9908286.

[2]  J. S. Seldenthuis,et al.  An all-electric single-molecule motor. , 2010, ACS nano.

[3]  G. Crooks.  Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Christopher Jarzynski,et al.  Illustrative example of the relationship between dissipation and relative entropy. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  K.-U. Stein.  Noise-induced error rate as limiting factory for energy per operation in digital ICs , 1977 .

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

[7]  Patrick R. Zulkowski,et al.  Optimal finite-time erasure of a classical bit. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

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

[11]  Stanislas Leibler,et al.  Speed, dissipation, and error in kinetic proofreading , 2012, Proceedings of the National Academy of Sciences.

[12]  C. Jarzynski,et al.  Information Processing and the Second Law of Thermodynamics: An Inclusive Hamiltonian Approach. , 2013, 1308.5001.

[13]  Pablo Sartori,et al.  Thermodynamics of Error Correction , 2015, 1504.06407.

[14]  Jeremy L. England,et al.  Minimum energetic cost to maintain a target nonequilibrium state. , 2017, Physical review. E.

[15]  Wojciech H. Zurek,et al.  Reversibility and stability of information processing systems , 1984 .

[16]  Udo Seifert.  Entropy production along a stochastic trajectory and an integral fluctuation theorem. , 2005, Physical review letters.

[17]  Todd R. Gingrich,et al.  Dissipation Bounds All Steady-State Current Fluctuations. , 2015, Physical review letters.

[18]  Juan M R Parrondo,et al.  Estimating dissipation from single stationary trajectories. , 2010, Physical review letters.

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

[20]  Momčilo Gavrilov.  High-Precision Test of Landauer’s Principle , 2017 .

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

[22]  Yuhai Tu,et al.  The energy-speed-accuracy tradeoff in sensory adaptation , 2012, Nature Physics.

[23]  Peter Salamon,et al.  Thermodynamic length and dissipated availability , 1983 .

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

[25]  Yonggun Jun,et al.  High-precision test of Landauer's principle in a feedback trap. , 2014, Physical review letters.

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

[27]  J. Crutchfield,et al.  Fluctuations When Driving Between Nonequilibrium Steady States , 2016, 1610.09444.

[28]  K.-U. Stein,et al.  Energy per logic operation in integrated circuits: definition and determination , 1976 .

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

[30]  R. Astumian,et al.  How molecular motors work – insights from the molecular machinist's toolbox: the Nobel prize in Chemistry 2016 , 2016, Chemical science.

[31]  J. Parrondo,et al.  Lower bounds on dissipation upon coarse graining. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  G. Crooks,et al.  Length of time's arrow. , 2008, Physical review letters.

[33]  J. Hopfield.  Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

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

[35]  Diana Marculescu,et al.  Power efficiency of voltage scaling in multiple clock, multiple voltage cores , 2002, ICCAD 2002.

[36]  J. Parrondo,et al.  Dissipation: the phase-space perspective. , 2007, Physical review letters.

[37]  M. Esposito.  Stochastic thermodynamics under coarse graining. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Anantha P. Chandrakasan,et al.  Low-power CMOS digital design , 1992 .

[39]  Surya Ganguli,et al.  A universal tradeoff between power, precision and speed in physical communication , 2016, ArXiv.

[40]  David A. Sivak,et al.  Thermodynamic metrics and optimal paths. , 2012, Physical review letters.

[41]  David A. Sivak,et al.  Toward the design principles of molecular machines , 2017, 1701.04868.

[42]  J. von Neumann,et al.  Probabilistic Logic and the Synthesis of Reliable Organisms from Unreliable Components , 1956 .

[43]  James P. Crutchfield,et al.  Refining Landauer’s Stack: Balancing Error and Dissipation When Erasing Information , 2020, Journal of Statistical Physics.

[44]  David A Leigh,et al.  Molecular machines with bio-inspired mechanisms , 2018, Proceedings of the National Academy of Sciences.

[45]  Sebastian Deffner,et al.  Optimal driving of isothermal processes close to equilibrium. , 2014, The Journal of chemical physics.

[46]  Lorenzo Alvisi,et al.  Modeling the effect of technology trends on the soft error rate of combinational logic , 2002, Proceedings International Conference on Dependable Systems and Networks.

[47]  Charles H. Bennett,et al.  Dissipation-error tradeoff in proofreading. , 1979, Bio Systems.

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

[49]  Pieter Rein ten Wolde,et al.  Thermodynamics of Computational Copying in Biochemical Systems , 2015, 1503.00909.

[50]  P. Benioff.  Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Application to Turing machines , 1982 .

[51]  C. Jarzynski.  Rare events and the convergence of exponentially averaged work values. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Christopher Jarzynski,et al.  Analysis of slow transitions between nonequilibrium steady states , 2015, 1507.06269.

[53]  L. Brillouin,et al.  Science and information theory , 1956 .

[54]  Pérès,et al.  Reversible logic and quantum computers. , 1985, Physical review. A, General physics.

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

[56]  Jeremy L. England,et al.  Statistical physics of self-replication. , 2012, The Journal of chemical physics.