- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Thermodynamics of Computations with Absolute Irreversibility, Unidirectional Transitions, and Stochastic Computation Times

Gonzalo Manzano1, Gülce Kardeş2,3, Édgar Roldán4, and David H. Wolpert3,4

  • 1Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC, Mallorca, Spain
  • 2University of Colorado, Boulder, Colorado 80309, USA
  • 3Santa Fe Institute, Santa Fe, New Mexico 87501, USA
  • 4ICTP—The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

PDF

Phys. Rev. X 14, 021026 – Published 13 May, 2024

DOI: https://doi.org/10.1103/PhysRevX.14.021026

Abstract

Developing a thermodynamic theory of computation is a challenging task at the interface of nonequilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times, unidirectional (possibly deterministic) transitions, and restricted initial conditions, features common in real-world computers. Here, we present a framework which tackles all such difficulties by extending the martingale theory of nonequilibrium thermodynamics to generic nonstationary Markovian processes, including those with broken detailed balance and/or absolute irreversibility. We derive several universal fluctuation relations and second-law-like inequalities that provide both lower and upper bounds on the intrinsic dissipation (mismatch cost) associated with any periodic process—in particular, the periodic processes underlying all current digital computation. Crucially, these bounds apply even if the process has stochastic stopping times, as it does in many computational machines. We illustrate our results with exhaustive numerical simulations of deterministic finite automata processing bit strings, one of the fundamental models of computation from theoretical computer science. We also provide universal equalities and inequalities for the acceptance probability of words of a given length by a deterministic finite automaton in terms of thermodynamic quantities, and outline connections between computer science and stochastic resetting. Our results, while motivated from the computational context, are applicable far more broadly.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

The exponential growth of computational power and the popularization of modern information technologies has led to a corresponding exponential increase in the associated energy consumption, introducing major challenges for sustainability. However, quantifying the energetic costs of computation even at the most elementary level is a difficult task. In particular, it requires a thermodynamic theory of computation applicable to systems out of equilibrium and affected by fluctuations from their environment. In this work, we make crucial steps for developing such a theory by providing a framework with key ingredients for understanding the fundamental relationship between a given computational task and the energetic resources needed to implement it physically.

By focusing on the resulting dynamics of a computation, we obtain suitable quantifiers for the dissipation incurred by any computer that performs a given task with minimal information about its physical details. To achieve these results, we extend techniques in stochastic thermodynamics to deal with the difficulties of describing computations, such as the breakdown of microscopic reversibility. In this context, we also put forward results that are best known in the mathematics of finance (martingale theory) that allow us to deal with computations that last an uncertain amount of time, as is most often the case in the real world. Our results comprise universal relations and bounds for the minimal energetic costs of generic computations, refining our understanding of the second law of thermodynamics and its relation to information.

We expect our work to be of broad interest in not only computational sciences and nonequilibrium thermodynamics but also areas such as biological physics, where our results may apply to descriptions of information processing by living systems.

Article Text

References (131)

  1. Ken Sekimoto, Stochastic Energetics, Vol. 799 (Springer, New York, 2010).
  2. Christopher Jarzynski, Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, Annu. Rev. Condens. Matter Phys. 2, 329 (2011).
  3. Udo Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  4. Naoto Shiraishi, Ken Funo, and Keiji Saito, Speed limit for classical stochastic processes, Phys. Rev. Lett. 121, 070601 (2018).
  5. Van Tuan Vo, Tan Van Vu, and Yoshihiko Hasegawa, Unified approach to classical speed limit and thermodynamic uncertainty relation, Phys. Rev. E 102, 062132 (2020).
  6. Tan Van Vu and Keiji Saito, Thermodynamic unification of optimal transport: Thermodynamic uncertainty relation, minimum dissipation, and thermodynamic speed limits, Phys. Rev. X 13, 011013 (2023).
  7. Andre C. Barato and Udo Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
  8. Todd R. Gingrich, Jordan M. Horowitz, Nikolay Perunov, and Jeremy L. England, Dissipation bounds all steady-state fluctuations, Phys. Rev. Lett. 116, 120601 (2016).
  9. Jordan M. Horowitz and Todd R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020).
  10. Yasuhiro Utsumi, Yasuchika Ito, Dimitry Golubev, and Ferdinand Peper, Computation time and thermodynamic uncertainty relation of Brownian circuits, arXiv:2205.10735.
  11. Raphaël Chetrite and Hugo Touchette, Nonequilibrium Markov processes conditioned on large deviations, in Annales Henri Poincaré, Vol. 16 (Springer, 2015), pp. 2005–2057, 10.1007/s00023-014-0375-8.
  12. Johannes Hoppenau, Daniel Nickelsen, and Andreas Engel, Level 2 and level 2.5 large deviation functionals for systems with and without detailed balance, New J. Phys. 18, 083010 (2016).
  13. Izaak Neri, Édgar Roldán, and Frank Jülicher, Statistics of infima and stopping times of entropy production and applications to active molecular processes, Phys. Rev. X 7, 011019 (2017).
  14. Raphaël Chétrite, Shamik Gupta, Izaak Neri, and Édgar Roldán, Martingale theory for housekeeping heat, Europhys. Lett. 124, 60006 (2019).
  15. Gonzalo Manzano, Rosario Fazio, and Édgar Roldán, Quantum martingale theory and entropy production, Phys. Rev. Lett. 122, 220602 (2019).
  16. Gonzalo Manzano, Diego Subero, Olivier Maillet, Rosario Fazio, Jukka P. Pekola, and Édgar Roldán, Thermodynamics of gambling demons, Phys. Rev. Lett. 126, 080603 (2021).
  17. Gonzalo Manzano and Édgar Roldán, Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines, Phys. Rev. E 105, 024112 (2022).
  18. Izaak Neri and Matteo Polettini, Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation, SciPost Phys. 14, 131 (2023).
  19. Édgar Roldán, Izaak Neri, Raphael Chetrite, Shamik Gupta, Simone Pigolotti, Frank Jülicher, and Ken Sekimoto, Martingales for physicists, arXiv:2210.09983.
  20. Marco Baiesi and Gianmaria Falasco, Inflow rate, a time-symmetric observable obeying fluctuation relations, Phys. Rev. E 92, 042162 (2015).
  21. Ivan Di Terlizzi and Marco Baiesi, Kinetic uncertainty relation, J. Phys. A 52, 02LT03 (2018).
  22. Christian Maes, Frenesy: Time-symmetric dynamical activity in nonequilibria, Phys. Rep. 850, 1 (2020).
  23. Harvey Leff and Andrew F. Rex, Maxwell’s Demon 2 Entropy, Classical and Quantum Information, Computing (CRC Press, Boca Raton, FL, 2002).
  24. Ryoichi Kawai, Juan M. R. Parrondo, and Christian Van den Broeck, Dissipation: The phase-space perspective, Phys. Rev. Lett. 98, 080602 (2007).
  25. Karel Proesmans, Jannik Ehrich, and John Bechhoefer, Finite-time Landauer principle, Phys. Rev. Lett. 125, 100602 (2020).
  26. Salambô Dago, Jorge Pereda, Nicolas Barros, Sergio Ciliberto, and Ludovic Bellon, Information and thermodynamics: Fast and precise approach to Landauer’s bound in an underdamped micromechanical oscillator, Phys. Rev. Lett. 126, 170601 (2021).
  27. David H. Wolpert and Artemy Kolchinsky, Thermodynamics of computing with circuits, New J. Phys. 22, 063047 (2020); see also updated version arXiv:1806.04103.
  28. Thomas E. Ouldridge and David H. Wolpert, Thermodynamics of deterministic finite automata operating locally and periodically, New J. Phys. 25, 123013 (2023).
  29. Gülce Kardeş and David Wolpert, Inclusive thermodynamics of computational machines, arXiv:2206.01165.
  30. Christopher Jarzynski, Hamiltonian derivation of a detailed fluctuation theorem, J. Stat. Phys. 98, 77 (2000).
  31. Massimiliano Esposito, Katja Lindenberg, and Christian Van den Broeck, Entropy production as correlation between system and reservoir, New J. Phys. 12, 013013 (2010).
  32. Sebastian Deffner and Christopher Jarzynski, Information processing and the second law of thermodynamics: An inclusive, Hamiltonian approach, Phys. Rev. X 3, 041003 (2013).
  33. Krzysztof Ptaszyński and Massimiliano Esposito, Entropy production in open systems: The predominant role of intraenvironment correlations, Phys. Rev. Lett. 123, 200603 (2019).
  34. Saar Rahav and Upendra Harbola, An integral fluctuation theorem for systems with unidirectional transitions, J. Stat. Mech. (2014) P10044.
  35. Arnab Pal and Saar Rahav, Integral fluctuation theorems for stochastic resetting systems, Phys. Rev. E 96, 062135 (2017).
  36. Daniel M. Busiello, Deepak Gupta, and Amos Maritan, Entropy production in systems with unidirectional transitions, Phys. Rev. Res. 2, 023011 (2020).
  37. Ken Hiura and Shin-ichi Sasa, Kinetic uncertainty relation on first-passage time for accumulated current, Phys. Rev. E 103, L050103 (2021).
  38. Charles Moslonka and Ken Sekimoto, Martingale-induced local invariance in progressive quenching, Phys. Rev. E 105, 044146 (2022).
  39. Kiyoshi Kanazawa, Tomohiko G. Sano, Takahiro Sagawa, and Hisao Hayakawa, Minimal model of stochastic athermal systems: Origin of non-Gaussian noise, Phys. Rev. Lett. 114, 090601 (2015).
  40. Massimiliano Esposito and Juan M. R. Parrondo, Stochastic thermodynamics of hidden pumps, Phys. Rev. E 91, 052114 (2015).
  41. Gonzalo Manzano, Jordan M. Horowitz, and Juan M. R. Parrondo, Quantum fluctuation theorems for arbitrary environments: Adiabatic and nonadiabatic entropy production, Phys. Rev. X 8, 031037 (2018).
  42. Lennart Dabelow, Stefano Bo, and Ralf Eichhorn, Irreversibility in active matter systems: Fluctuation theorem and mutual information, Phys. Rev. X 9, 021009 (2019).
  43. Laura Tociu, Étienne Fodor, Takahiro Nemoto, and Suriyanarayanan Vaikuntanathan, How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure, and biased interactions, Phys. Rev. X 9, 041026 (2019).

  44. However, we emphasize that our theory is also applicable to the more standard scenario, such as when LDB is verified.

  45. See Chap. 4 in Ref. [19] for rigorous mathematical definitions and mathematical properties of stopping times, and examples of stopping times in physics (e.g., first-passage times).

  46. A version of this result even holds for quantum thermodynamic processes. For further discussion of the concept of mismatch cost in stochastic thermodynamics of computation, see Refs. [47, 48, 49, 50].

  47. Artemy Kolchinsky and David H. Wolpert, Dependence of dissipation on the initial distribution over states, J. Stat. Mech. (2017) 083202.
  48. D. H. Wolpert, A. Kolchinsky, and J. A. Owen, A space-time tradeoff for implementing a function with master equation dynamics, Nat. Commun. 10, 1727 (2019).
  49. Artemy Kolchinsky and David H. Wolpert, Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes, Phys. Rev. E 104, 054107 (2021).
  50. Paul M. Riechers and Mile Gu, Initial-state dependence of thermodynamic dissipation for any quantum process, Phys. Rev. E 103, 042145 (2021).

  51. An analogous notion of stochastic distinguishability was introduced in Ref. [16], in the context of forward and time-reversed nonstationary dynamics.

  52. Massimiliano Esposito and Christian Van den Broeck, Three detailed fluctuation theorems, Phys. Rev. Lett. 104, 090601 (2010).
  53. Takahiro Hatano and Shin-ichi Sasa, Steady-state thermodynamics of Langevin systems, Phys. Rev. Lett. 86, 3463 (2001).

  54. In general, in this paper, ⟨A(t)|x[0,s]⟩=E[A(t)|x[0,s]] is an average of functional A over all computational trajectories with the condition of x[0,s]=x0,…,xs to be fixed to a given sequence.

  55. Here D(ρ0∥ρ¯τ)=∑xρ0(x)ln[ρ0(x)/ρ¯τ(x)]≥0 is the Kullback-Leibler (KL) quantifying the “distance” between the initial distribution of the computer’s state ρ0 and the distribution ρ¯τ of the auxiliary computational process at the limit time τ.

  56. I. Di Terlizzi, M. Gironella, D. Herráez-Aguilar, T. Betz, F. Monroy, M. Baiesi, and F. Ritort, Variance sum rule for entropy production, Science 383, 971 (2024).
  57. T. Nishiyama and Y. Hasegawa, Upper bound for entropy production in Markov processes, Phys. Rev. E 108, 044139 (2023).
  58. Domingos S. P. Salazar, Upper bound for quantum entropy production from entropy flux, Phys. Rev. E 105, L042101 (2022).
  59. Juan M. R. Parrondo, Jordan M. Horowitz, and Takahiro Sagawa, Thermodynamics of information, Nat. Phys. 11, 131 (2015).
  60. Takahiro Sagawa, Thermodynamic and logical reversibilities revisited, J. Stat. Mech. (2014) P03025.
  61. Philipp Strasberg, Javier Cerrillo, Gernot Schaller, and Tobias Brandes, Thermodynamics of stochastic Turing machines, Phys. Rev. E 92, 042104 (2015).
  62. Artemy Kolchinsky and David H. Wolpert, Thermodynamic costs of Turing machines, Phys. Rev. Res. 2, 033312 (2020).
  63. Udo Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  64. R. Kawai, J. M. R. Parrondo, and C. Van den Broeck, Dissipation: The phase-space perspective, Phys. Rev. Lett. 98, 080602 (2007).
  65. J. A. Owen, A. Kolchinsky, and D. H. Wolpert, Number of hidden states needed to physically implement a given conditional distribution, New J. Phys. 21, 013022 (2019).

  66. Note that formula for F is indeed linear in ϱt.

  67. David H. Wolpert, The free energy requirements of biological organisms; implications for evolution, Entropy 18, 219 (2016).
  68. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Jonh Wiley and Sons, New York, 2012).

  69. Here we are interested in the marginal prior distribution over computational states x∈X only, not over the set Y containing hidden states.

  70. Farita Tasnim and David H. Wolpert, Stochastic thermodynamics of multiple co-evolving systems—Beyond multipartite processes, Entropy 25, 1078 (2023).
  71. Yoshitsugu Oono and Marco Paniconi, Steady state thermodynamics, Prog. Theor. Phys. Suppl. 130, 29 (1998).
  72. Massimiliano Esposito and Christian Van den Broeck, Three faces of the second law. I. Master equation formulation, Phys. Rev. E 82, 011143 (2010).

  73. Here we will not consider the eventual erasure of the input tape after the computation ends, but we focus on the thermodynamic costs and dissipation due to the computing process itself, using the information contained in the tape. Such eventual erasure costs are independent of the mismatch costs considered here and might be calculated on a separate basis.

  74. Andre C. Barato and Udo Seifert, Stochastic thermodynamics with information reservoirs, Phys. Rev. E 90, 042150 (2014).

  75. Notice that the DTMC transition probabilities P(xt+1|xt) among the (coarse-grained) computational states in X are given by marginalizing a fine-grained conditional distribution P(yt+1|yt), where y=(x,s,…) over s, namely the current symbol being read, and where the update function f defining the DFA specifies P[xt+1|(xs,st)]. As a consequence, the transition probabilities P(xt+1|xt) are time independent and fixed along the entire computational process.

  76. This means that one cannot model a given DFA as some specific (and therefore fixed width) circuit, in general. The DFA will have properties that are not captured by that circuit. In this sense, individual DFAs are computationally more powerful than individual circuits.

  77. Note that by “P(j|i)” we do not mean the Bayesian inverse of the forward transition matrix P(i|j); rather, we mean that forward transition matrix evaluated for a transposed choice of the initial and final states.

  78. This can be easily checked from ∑jP¯(i|j)r′(j)=∑jP(j|i)r(i)=r(i), which immediately implies [W¯]r′=r.

  79. E. T. Jaynes, Probability Theory. The Logic of Science (Cambridge University Press, New York, USA, 2003).
  80. Francesco Buscemi and Valerio Scarani, Fluctuation theorems from Bayesian retrodiction, Phys. Rev. E 103, 052111 (2021).
  81. Jacopo Surace and Matteo Scandi, State retrieval beyond Bayes’ retrodiction, Quantum 7, 990 (2023).
  82. Gonzalo Manzano, Jordan M. Horowitz, and Juan M. R. Parrondo, Nonequilibrium potential and fluctuation theorems for quantum maps, Phys. Rev. E 92, 032129 (2015).
  83. Herbert Spohn, Entropy production for quantum dynamical semigroups, J. Math. Phys. 19, 1227 (1978).
  84. Yûto Murashita, Ken Funo, and Masahito Ueda, Nonequilibrium equalities in absolutely irreversible processes, Phys. Rev. E 90, 042110 (2014).
  85. Ken Funo, Yûto Murashita, and Masahito Ueda, Quantum nonequilibrium equalities with absolute irreversibility, New J. Phys. 17, 075005 (2015).
  86. Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda, and Y. Nakamura, Information-to-work conversion by Maxwell’s demon in a superconducting circuit quantum electrodynamical system, Nat. Commun. 9, 1291 (2018).
  87. David Williams, Probability with Martingales (Cambridge University Press, Cambridge, England, 1991).
  88. J. L. Doob, Stochastic Processes (Wiley, New York, 1990).
  89. John A. C. Albay, Yonggun Jun, and Pik-Yin Lai, Winning strategies of a gambling demon in a Brownian particle under a squeezing potential, Phys. Rev. Res. 5, 023115 (2023).
  90. M. Ribezzi-Crivellari and F. Ritort, Large work extraction and the Landauer limit in a continuous Maxwell demon, Nat. Phys. 15, 660 (2019).
  91. M. Rico-Pasto, R. K. Schmitt, M. Ribezzi-Crivellari, J. M. R. Parrondo, H. Linke, J. Johansson, and F. Ritort, Dissipation reduction and information-to-measurement conversion in DNA pulling experiments with feedback protocols, Phys. Rev. X 11, 031052 (2021).
  92. Ilya Prigogine, Etude thermodynamique des phénomènes irréversibles, Bull. Acad. R. Belg. Cl. Sci. 31, 600 (1945).
  93. L. Onsager and S. Machlup, Fluctuations and irreversible processes, Phys. Rev. 91, 1505 (1953).
  94. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Minimum dissipation principle in stationary non-equilibrium states, J. Stat. Phys. 116, 831 (2004).
  95. J. W. Carlyle and A. Paz, Realizations by stochastic finite automata, J. Comput. Syst. Sci. 5, 26 (1971).
  96. Jorge Castro and Ricard Gavaldà, Learning probability distributions generated by finite-state machines, in Topics in Grammatical Inference (Springer, Berlin, 2016), pp. 113–142.
  97. Izaak Neri, Édgar Roldán, Simone Pigolotti, and Frank Jülicher, Integral fluctuation relations for entropy production at stopping times, J. Stat. Mech. (2019) 104006.
  98. Martin R. Evans, Satya N. Majumdar, and Grégory Schehr, Stochastic resetting and applications, J. Phys. A 53, 193001 (2020).
  99. Shamik Gupta and Arun M. Jayannavar, Stochastic resetting: A (very) brief review, Front. Phys. 10, 789097 (2022).
  100. Ofir Tal-Friedman, Arnab Pal, Amandeep Sekhon, Shlomi Reuveni, and Yael Roichman, Experimental realization of diffusion with stochastic resetting, J. Phys. Chem. Lett. 11, 7350 (2020).
  101. Édgar Roldán, Ana Lisica, Daniel Sánchez-Taltavull, and Stephan W. Grill, Stochastic resetting in backtrack recovery by RNA polymerases, Phys. Rev. E 93, 062411 (2016).
  102. Paul C. Bressloff, Modeling active cellular transport as a directed search process with stochastic resetting and delays, J. Phys. A 53, 355001 (2020).
  103. Antoine Bérut, Artak Arakelyan, Artyom Petrosyan, Sergio Ciliberto, Raoul Dillenschneider, and Eric Lutz, Experimental verification of Landauer’s principle linking information and thermodynamics, Nature (London) 483, 187 (2012).
  104. Yonggun Jun, Momčilo Gavrilov, and John Bechhoefer, High-precision test of Landauer’s principle in a feedback trap, Phys. Rev. Lett. 113, 190601 (2014).
  105. S. Ciliberto, Experiments in stochastic thermodynamics: Short history and perspectives, Phys. Rev. X 7, 021051 (2017).
  106. Ignacio A. Martínez, Édgar Roldán, Luis Dinis, and Raúl A. Rica, Colloidal heat engines: A review, Soft Matter 13, 22 (2017).
  107. J. P. Pekola, D. S. Golubev, and D. V. Averin, Maxwell’s demon based on a single qubit, Phys. Rev. B 93, 024501 (2016).
  108. Salambô Dago and Ludovic Bellon, Dynamics of information erasure and extension of Landauer’s bound to fast processes, Phys. Rev. Lett. 128, 070604 (2022).
  109. Sidney Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
  110. Vladimir Y. Chernyak, Michael Chertkov, and Christopher Jarzynski, Path-integral analysis of fluctuation theorems for general Langevin processes, J. Stat. Mech. (2006) P08001.
  111. Gatien Verley, Raphaël Chétrite, and David Lacoste, Inequalities generalizing the second law of thermodynamics for transitions between nonstationary states, Phys. Rev. Lett. 108, 120601 (2012).
  112. Arya Datta, Patrick Pietzonka, and Andre C. Barato, Second law for active heat engines, Phys. Rev. X 12, 031034 (2022).
  113. Faezeh Khodabandehlou, Christian Maes, and Karel Netočný, A Nernst heat theorem for nonequilibrium jump processes, J. Chem. Phys. 158, 204112 (2023).
  114. Pritha Dolai, Christian Maes, and Karel Netočný, Calorimetry for active systems, SciPost Phys. 14, 126 (2023).
  115. Yaakov Benenson, Biomolecular computing systems: Principles, progress and potential, Nat. Rev. Genet. 13, 455 (2012).
  116. Athel Cornish-Bowden, Fundamentals of Enzyme Kinetics (John Wiley and Sons, New York, 2013).
  117. Julien O. Dubuis, Gašper Tkačik, Eric F. Wieschaus, Thomas Gregor, and William Bialek, Positional information, in bits, Proc. Natl. Acad. Sci. U.S.A. 110, 16301 (2013).
  118. Chunhe Li and Jin Wang, Quantifying cell fate decisions for differentiation and reprogramming of a human stem cell network: Landscape and biological paths, PLoS Comput. Biol. 9, e1003165 (2013).
  119. Jin Wang, Landscape and flux theory of non-equilibrium dynamical systems with application to biology, Adv. Phys. 64, 1 (2015).
  120. Ivana Ban, Lucija Tomašić, Marianna Trakala, Iva M. Tolić, and Nenad Pavin, Proliferative advantage of specific aneuploid cells drives evolution of tumor karyotypes, Biophys. J. 122, 632 (2023).
  121. Christopher Battle, Chase P. Broedersz, Nikta Fakhri, Veikko F. Geyer, Jonathon Howard, Christoph F. Schmidt, and Fred C. MacKintosh, Broken detailed balance at mesoscopic scales in active biological systems, Science 352, 604 (2016).
  122. Étienne Fodor, Cesare Nardini, Michael E. Cates, Julien Tailleur, Paolo Visco, and Frédéric van Wijland, How far from equilibrium is active matter?, Phys. Rev. Lett. 117, 038103 (2016).
  123. Édgar Roldán, Jérémie Barral, Pascal Martin, Juan M. R. Parrondo, and Frank Jülicher, Quantifying entropy production in active fluctuations of the hair-cell bundle from time irreversibility and uncertainty relations, New J. Phys. 23, 083013 (2021).
  124. José A. Morin, Francisco J. Cao, José M. Lázaro, J. Ricardo Arias-Gonzalez, José M. Valpuesta, José L. Carrascosa, Margarita Salas, and Borja Ibarra, Mechano-chemical kinetics of DNA replication: Identification of the translocation step of a replicative DNA polymerase, Nucleic Acids Res. 43, 3643 (2015).
  125. Annwesha Dutta, Gunter M. Schütz, and Debashish Chowdhury, Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective, Phys. Rev. E 101, 032402 (2020).
  126. David H. Wolpert, The stochastic thermodynamics of computation, J. Phys. A 52, 193001 (2019).
  127. Philipp Strasberg and Massimiliano Esposito, Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining, Phys. Rev. E 95, 062101 (2017).
  128. Robert S. Whitney, Non-Markovian quantum thermodynamics: Laws and fluctuation theorems, Phys. Rev. B 98, 085415 (2018).
  129. Cillian Cockrell and Ian J. Ford, Stochastic thermodynamics in a non-Markovian dynamical system, Phys. Rev. E 105, 064124 (2022).
  130. A. Gomez-Marin, J. M. R. Parrondo, and C. Van den Broeck, Lower bounds on dissipation upon coarse graining, Phys. Rev. E 78, 011107 (2008).
  131. Édgar Roldán and Juan M. R. Parrondo, Estimating dissipation from single stationary trajectories, Phys. Rev. Lett. 105, 150607 (2010).

Outline

Information

Phys. Rev. X 14, 021026– Published 13 May, 2024
  • Received 25 July 2023
  • Revised 16 February 2024
  • Accepted 14 March 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation