Excerpt

Introduction

Interest in the thermodynamics of computation has revived in recent years, driven by developments in science, economics, and technology. Given the consequences of the growing demand for computational power, the idea of reducing the energy cost of computations has gained new importance (DeBenedictis, Mee, and Frank 2017; Frank 2017). Simultaneously, many biological networks are now interpreted as informationprocessing or computational systems constrained by their underlying thermodynamics (Andrieux and Gaspard 2008; Lan et al. 2012; Mehta and Schwab 2012; Ito and Sagawa 2015; Govern and ten Wolde 2014; Barato, Hartich, and Seifert 2014; Mehta, Lang, and Schwab 2016; ten Wolde et al. 2016; Ouldridge and ten Wolde 2017; Ouldridge, Govern, and ten Wolde 2017; Barato and Seifert 2017). Indeed, some suggest (Bennett 1982; Adleman 1994; Organick et al. 2018) that lowcost, high-density biological systems may help to mitigate the rising demand for computational power and the “end” of Moore’s law of exponential growth in the density of transistors (Frank 2017).

In this chapter, we address widespread misconceptions about thermodynamics and the thermodynamics of computation, using biomolecular systems as a conceptual crutch. In particular, we argue against the general perception that a measurement or copy operation can be performed at no cost; against the emphasis placed on the significance of erasure operations; and against the careless discussion of heat and work. Although not universal, these misconceptions are sufficiently prevalent (particularly within interdisciplinary contexts) to warrant a detailed discussion. In the process, we argue that representing fundamental processes explicitly is a useful tool, serving to demystify key concepts.

We give first a brief overview of thermodynamics, then the history of the thermodynamics of computation—particularly in terms of copy and measurement operations inherent to classic thought experiments. Subsequently, we analyze these ideas via an explicit biochemical representation of the entire cycle of Szilard’s engine. In doing so, we show that molecular computation is both a promising engineering paradigm and a valuable tool in providing fundamental understanding.

Bibliography

Adleman, L. M. 1994. “Molecular Computation of Solutions to Combinatorial Problems.” Science 266:1021–1024.

Andrieux, D., and P. Gaspard. 2008. “Nonequilibrium Generation of Information in Copolymerization Processes.” Proceedings of the National Academy of Sciences of the United States of America 105:9516–9521.

————. 2013. “Information Erasure in Copolymers.” Europhysics Letters 103:30004.

Atkins, P. 2010. The Laws of Thermodynamics: A Very Short Introduction. Oxford: Oxford University Press.

Barato, A. C., D. Hartich, and U. Seifert. 2014. “Efficiency of Cellular Information Processing.” New Journal of Physics 16:103024.

Barato, A. C., and U. Seifert. 2017. “Coherence of Biochemical Oscillations Is Bounded by Driving Force and Network Topology.” Physical Review E 95:062409.

Bennett, C. H. 1982. “The Thermodynamics of Computation—A Review.” International Journal of Theoretical Physics 21:905–940.

————. 2003. “Notes on Landauer’s Principle, Reversible Computation, and Maxwell’s Demon.” Studies in History and Philosophy of Modern Physics 34:501–510.

Bérut, A., A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz. 2012. “Experimental Verification of Landauer’s Principle Linking Information and Thermodynamics.” Nature 483:187–189.

Boyd, A. B., D. Mandal, and J. P. Crutchfield. 2016. “Identifying Functional Thermodynamics in Autonomous Maxwellian Ratchets.” New Journal of Physics 18:023049.

Brillouin, L. 1951. “Maxwell’s Demon Cannot Operate: Information and Entropy. I.” Journal of Applied Physics 22:334–337.

Brittain, R. A., N. S. Jones, and T. E. Ouldridge. 2018. Biochemical Szilard Engines for Memory-Limited Inference. arXiv: 1812.08401 [cond-mat.stat-mech].

Bub, J. 2001. “Maxwell’s Demon and the Thermodynamics of Computation.” Studies in History and Philosophy of Modern Physics 32:569–579.

Chapman, A., and A. Miyake. 2015. “How an Autonomous Quantum Maxwell Demon Can Harness Correlated Information.” Physical Review E 92:062125.

Chen, Y.-J., N. Dalchau, N. Srinivas, A. Phillips, L. Cardelli, D. Solveichik, and G. Seelig. 2013. “Programmable Chemical Controllers Made from DNA.” Nature Nanotechnology 8:755–762.

Crooks, G. E. 1999. “Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences.” Physics Review E 60:2721–2726.

DeBenedictis, E. P., J. K. Mee, and M. P. Frank. 2017. “The Opportunities and Controversies of Reversible Computing.” Computer 50:76–80.

Deffner, S. 2015. “Viewpoint: Exorcising Maxwell’s Demon.” Physics 8:127.

Deshpande, A., M. Gopalkrishnan, T. E. Ouldridge, and N. S. Jones. 2017. “Designing the Optimal Bit: Balancing Energetic Cost, Speed and Reliability.” Proceedings of the Royal Society of London, Series A 473 (2204).

Dillenschneider, R., and E. Lutz. 2009. “Memory Erasure in Small Systems.” Physical Review Letters 102:210601.

Dougal, R. C. 2016. “Kelvin, Thermodynamics and the Natural World.” In Kelvin, Maxwell, Clausius and Tait: The Correspondence of James Clerk Maxwell, edited by M. W. Collins, R. C. Dougal, C. Koenig, and I. S. Ruddock, 135–151. WIT Press.

Esposito, M., and C. Van den Broeck. 2011. “Second Law and Landauer Principle Far from Equilibrium.” Europhysics Letters 95:40004.

Fahn, P. N. 1996. “Maxwell’s Demon and the Entropy Cost of Information.” Foundations of Physics 26:71–93.

Feynman, R. P. 1998. Feynman Lectures on Computation. New York: Addison-Wesley.

Frank, M. P. 2017. “Throwing Computing into Reverse.” IEEE Spectrum 54:32–37.

Govern, C. C., and P. R. ten Wolde. 2014. “Optimal Resource Allocation in Cellular Sensing Systems.” Proc. Nat. Acad. Sci. USA 111:17486–17491.

Grochow, J. A., and D. H. Wolpert. 2018. “Beyond Number of Bit Erasures: New Complexity Questions Raised by Recently Discovered Thermodynamic Costs of Computation.” SIGACT News 49:33–56.

Hong, J., B. Lambson, S. Dhuey, and J. Bokor. 2016. “Experimental Test of Landauer’s Principle in Single-Bit Operations on Nanomagnetic Memory Bits.” Science Advances 2:e1501492.

Horowitz, J. M., T. Sagawa, and J. M. R. Parrondo. 2013. “Imitating Chemical Motors with Optimal Information Motors.” Physical Review Letters 111:010602.

Horowitz, J., and C. Jarzynski. 2008. “Comment on ‘Failure of the Work-Hamiltonian Connection for Free-Energy Calculations’.” Physical Review Letters 101:098901.

Huang, K. 1987. Statistical Mechanics. Second Edition. New York: John Wiley & Sons, Inc.

Ito, S., and T. Sagawa. 2015. “Maxwell’s Demon in Biochemical Signal Transduction with Feedback Loop.” Nature Communications 6:7498.

Jarzynski, C. 1997. “Nonequilibrium Equality for Free Energy Differences.” Phys. Rev. Lett. 78:2690–2693.

Jaynes, E. T. 1957. “Information Theory and Statistical Mechanics.” Physical Review 106:620–630.

Jun, Y., M. Gavrilov, and J. Bechhoefer. 2014. “High-Precision Test of Landauer’s Principle in a Feedback Trap.” Physical Review Letters 113:190601.

Kolchinsky, A., and D. H. Wolpert. 2017. “Dependence of Dissipation on the Initial Distribution over States.” Journal of Statistical Mechanics 2017:083202.

Koski, J. V., V. F. Maisi, T. Sagawa, and J. P. Pekola. 2014. “Experimental Observation of the Role of Mutual Information in the Nonequilibrium Dynamics of a Maxwell Demon.” Physical Review Letters 113:030601.

Krishnamurthy, S., and E. Smith. 2017. “Solving Moment Hierarchies for Chemical Reaction Networks.” Journal of Physics A 50:425002.

Ladyman, J., S. Presnell, A. J. Short, and B. Groisman. 2007. “The Connection between Logical and Thermodynamic Irreversibility.” Studies in History and Philosophy of Modern Physics 38:58–79.

Lambson, B., D. Carlton, and J. Bokor. 2011. “Exploring the Thermodynamic Limits of Computation in Integrated Systems: Magnetic Memory, Nanomagnetic Logic, and the Landauer Limit.” Physical Review Letters 107:010604.

Lan, G., P. Sartori, S. Neumann, V. Sourjik, and Y. Tu. 2012. “The Energy–Speed–Accuracy Trade-Off in Sensory Adaptation.” Nature Physics 8:422–428.

Landauer, R. 1961. “Irreversibility and Heat Generation in the Computing Process.” IBM Journal of Research and Development 5:183–191.

————. 1991. “Information Is Physical.” Physics Today 44:23–29.

Mandal, D., and C. Jarzynski. 2012. “Work and Information Processing in a Solvable Model of Maxwell’s Demon.” Proceedings of the National Academy of Sciences of the United States of America 109:11641–11645.

Maroney, O. J. E. 2005. “The (Absence of a) Relationship between Thermodynamic and Logical Reversibility.” Studies in History and Philosophy of Modern Physics 36:355–374.

Maruyama, K., F. Nori, and V. Vedral. 2009. “Colloquium: The Physics of Maxwell’s Demon and Information.” Reviews of Modern Physics 81.

McGrath, T., N. S. Jones, P. R. ten Wolde, and T. E. Ouldridge. 2017. “Biochemical Machines for the Interconversion of Mutual Information and Work.” Physics Review Letters 118:028101.

Mehta, P., A. H. Lang, and D. J. Schwab. 2016. “Landauer in the Age of Synthetic Biology: Energy Consumption and Information Processing in Biochemical Networks.” Journal of Statistical Physics 162:1153–1166.

Mehta, P., and D. J Schwab. 2012. “Energetic Costs of Cellular Computation.” Proceedings of the National Academy of Sciences of the United States of America 109:17978–17982.

Nelson, P. 2004. Biological Physics: Energy, Information, Life. New York: W. H. Freeman.

Norton, J. D. 2005. “Eaters of the Lotus: Landauer’s Principle and the Return of Maxwell’s Demon.” Stud. Hist. Philos. M. P. 36:375–411.

Organick, L., S. D. Ang, Y.-J. Chen, R. Lopez, S. Yekhanin, K. Makarychev, M. Z. Racz, et al. 2018. “Random Access in Large-Scale DNA Data Storage.” Nature Biotechnology 36:242–248.

Ouldridge, T. E. 2018. “The Importance of Thermodynamics for Molecular Systems and the Importance of Molecular Systems for Thermodynamics.” Natural Computing 17:3–29.

Ouldridge, T. E., C. C. Govern, and P. R. ten Wolde. 2017. “The Thermodynamics of Computational Copying in Biochemical Systems.” Physical Review X 7:021004.

Ouldridge, T. E., and P. R. ten Wolde. 2017. “Fundamental Costs in the Production and Destruction of Persistent Polymer Copies.” Physical Review Letters 118:158103.

Owen, J. A., A. Kolchinsky, and D. H. Wolpert. 2011. “Number of Hidden States Needed to Physically Implement a Given Conditional Distribution.” New Journal of Physics 21.

Parrondo, J. M., J. M. Horowitz, and T. Sagawa. 2015. “Thermodynamics of Information.” Natural Physics 11:131–139.

Plenio, M. B., and V. Vitelli. 2001. “The Physics of Forgetting: Landauer’s Erasure Principle and Information Theory.” Contemporary Physics 42:25–60.

Plesa, T. 2018. Stochastic Approximation of High-Molecular by Bi-Molecular Reactions. arXiv: 1811.02766 [q-bio.MN].

Qian, L., D. Soloviechick, and E. Winfree. 2011. “Efficient Turing-universal computation with DNA polymers.” DNA 16, LNCS 6518:123–140.

Rao, R., and M. Esposito. 2016. “Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics.” Physical Review X 6:041064.

————. 2018. “Conservation Laws and Work Fluctuation Relations in Chemical Reaction Networks.” The Journal of Chemical Physics 149:245101.

Sagawa, T. 2014. “Thermodynamic and Logical Reversibilities Revisited.” Journal of Statistical Mechanics: P03025.

Sagawa, T., and M. Ueda. 2009. “Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure.” Phys. Rev. Lett. 102:250602.

Schmiedl, T., and U. Seifert. 2007. “Stochastic Thermodynamics of Chemical Reaction Networks.” Journal of Chemical Physics 126:044101.

Seifert, U. 2005. “Entropy Production Along a Stochastic Trajectory and an Integral Fluctuation Theorem.” Physical Review Letters 95:040602.

————. 2011. “Stochastic Thermodynamics of Single Enzymes and Molecular Motors.” European Physical Journal E 34:26.

Shannon, C. E., and W. Weaver. 1949. The Mathematical Theory of Communication. Champaign: University of Illinois Press.

Srinivas, N., J. Parkin, G. Seelig, E. Winfree, and D. Soloveichik. 2017. “Enzyme-Free Nucleic Acid Dynamical Systems.” Science 358:eaal2052.

Stock, A. M., V. L. Robinson, and P. N. Goudreau. 2000. “Two-Component Signal Transduction.” Annual Review of Biochemistry 69:183–215.

Stopnitzky, E., S. Still, T. E. Ouldridge, and L. Altenberg. 2019. “Physical Limitations of Work Extraction from Temporal Correlations.” In The Energetics of Computing in Life and Machines, edited by D. H. Wolpert, C. Kempes, P. F. Stadler, and J. A. Grochow.

Szilard, L. 1964. “On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings.” Behavioral Science 9:301–310.

ten Wolde, P. R., N. B. Becker, T. E. Ouldridge, and Mugler A. 2016. “Fundamental Limits to Cellular Sensing.” Journal of Statistical Physics 162:1395–1424.

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