Finite-Time Landauer Principle

Proesmans, Karel; Ehrich, Jannik; Bechhoefer, John

doi:10.1103/physrevlett.125.100602

Cited by 114 publications

(109 citation statements)

References 39 publications

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“…Nevertheless, the Langevin-Smoluchowski limit remains a stepping stone for analytical investigations based on multiscale perturbation theory [103]. In addition, the solution of Landauer's optimal control problem in the Langevin-Smoluchowski limit is also the basis for the analysis of erasure when the bit of information is conceptualized as a macro-state specified by coarse graining the measure of a physical system with microscopic dynamics governed by (62) [108]. Thus, in a broad sense, Schrödinger's vision of an optimal stochastic mass transport problem between target states offers a powerful theoretical framework for conceptualizing transitions in stochastic thermodynamics.…”

Section: Landauer's Principle In the Context Of Langevin Dynamicsmentioning

confidence: 99%

E. Schrödinger’s 1931 paper “On the Reversal of the Laws of Nature” [“Über die Umkehrung der Naturgesetze”, Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 8 N9 144–153]

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Muratore-Ginanneschi

Schwieger

2021

EPJ H

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We present an English translation of Erwin Schrödinger’s paper on “On the Reversal of the Laws of Nature‘’. In this paper, Schrödinger analyses the idea of time reversal of a diffusion process. Schrödinger’s paper acted as a prominent source of inspiration for the works of Bernstein on reciprocal processes and of Kolmogorov on time reversal properties of Markov processes and detailed balance. The ideas outlined by Schrödinger also inspired the development of probabilistic interpretations of quantum mechanics by Fényes, Nelson and others as well as the notion of “Euclidean Quantum Mechanics” as probabilistic analogue of quantization. In the second part of the paper, Schrödinger discusses the relation between time reversal and statistical laws of physics. We emphasize in our commentary the relevance of Schrödinger’s intuitions for contemporary developments in statistical nano-physics.

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Section: Landauer's Principle In the Context Of Langevin Dynamicsmentioning

confidence: 99%

E. Schrödinger’s 1931 paper “On the Reversal of the Laws of Nature” [“Über die Umkehrung der Naturgesetze”, Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 8 N9 144–153]

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Muratore-Ginanneschi

Schwieger

2021

EPJ H

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“…Further, in 2011, Aurell, et al expanded the set of exactly solvable minimum-work protocols to a more general class of problems by finding a clever mapping of the stochastic differential equations to a set of deterministic transport equations [107,108]. While this work provided a new means of analyzing such problems, aside from some notable recent results regarding a finite-time Landauer limit [104,105], the study of analytically tractable solutions in optimal control of stochastic systems has seen little progress since. Primarily, this is due to the intrinsic difficulty in solving the general minimization problem in (2.54).…”

Section: Control In Microscopic Nonequilibrium Systemsmentioning

confidence: 99%

“…Recent work on optimal bit erasure[104,105] enforces a constraint on the final probability distribution rather than requiring that the control parameter reaches a particular final value.…”

mentioning

confidence: 99%

Dissipation and Control in Microscopic Nonequilibrium Systems

Large¹

2021

Springer Theses

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Quantifying the flow of energy, entropy, and information within and through nonequilibrium systems remains a central challenge in understanding the microscopic physics of biological systems. Over the past two and a half decades, parallel developments in the fields of theoretical stochastic thermodynamics and single-molecule experiments have made tremendous steps towards this end, advancing our understanding of the fundamental physical limitations and constraints faced by biological systems in vivo. Central in this focus are molecular machines: nanoscale protein complexes which interconvert between different forms of energy to perform useful functions to the cell. While single-molecule experiments on molecular machines have predicted impressively high efficiencies, much is still unknown about their performance in vivo. In this thesis we build upon these primitives, largely by making use of near-equilibrium phenomenological models to simplify and make tractable the problem of quantifying dissipation in molecular machines and predicting the operational modes which are imperative to minimizing their dissipation. By exploring the relevance of near-equilibrium models in the experimental investigation of a DNA hairpin, we find that such an approach can provide utility in understanding the strategies to reduce dissipation in nonequilibrium processes. However, single-molecule manipulations are significantly separated from the in vivo dynamics of molecular machines, and thus for the remainder of the thesis we expand upon this approach in various ways, generalizing the existing theoretical framework to more closely parallel the dynamics of molecular machines. By incorporating the inter-system feedback present in molecular machines, we find that familiar intuitions about how excess work and entropy production are related break down. Finally, we derive a phenomenological expression for the energy flows communicated within the components of a mechanochemical molecular machine. Ultimately, our analysis shows that intersystem feedback can lead to nonvanishing energy flows which are the manifestation of a Maxwell demon in the molecular machine itself.

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“…A common aim is to minimize average dissipated work. This is important for optimal bit erasure [10,11,12], as well as experimental measurements of the equilibrium free energy of biomolecules from nonequilibrium force pulling experiments and simulations [13,9,14]. Other targets include protocols that maximize thermodynamic efficiency for synthetic [15,16] and biological [17] nanoengines and protocols minimize dissipated heat, for example in bit flipping operations [18,19].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of nonequilibrium systems through automatic differentiation

Engel¹,

Smith²,

Brenner³

2022

Preprint

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Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, both in nanotechnology and biology. Progress in computing optimal protocols has thus far been limited to either simple systems or near-equilibrium evolution. Here, we present an approach for computing optimal protocols based on automatic differentiation. Our methodology is applicable to complex systems and multidimensional protocols and is valid arbitrarily far from equilibrium. We validate our method by reproducing theoretical optimal protocols for a Brownian particle in a time-varying harmonic trap. We also compute departures from near-equilibrium behaviour for magnetization reversal on an Ising lattice and for barrier crossing driven by a harmonic trap, which has been used to represent a range of biological processes including biomolecular unfolding reactions. Algorithms based on automatic differentiation outperform the near-equilibrium theory for far-from-equilibrium magnetization reversal and driven barrier crossing. The optimal protocol for crossing an energy landscape barrier of 10k B T is found to hasten the approach to, and slow the departure from, the barrier region compared to the near-equilibrium theoretical protocol.

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Finite-Time Landauer Principle

Cited by 114 publications

References 39 publications

E. Schrödinger’s 1931 paper “On the Reversal of the Laws of Nature” [“Über die Umkehrung der Naturgesetze”, Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 8 N9 144–153]

E. Schrödinger’s 1931 paper “On the Reversal of the Laws of Nature” [“Über die Umkehrung der Naturgesetze”, Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 8 N9 144–153]

Dissipation and Control in Microscopic Nonequilibrium Systems

Optimal control of nonequilibrium systems through automatic differentiation

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