A Simple Derivation of Crooks Relation

Chejne, Farid; Moukalled, F.; Gómez, Carlos Andrés

doi:10.5541/ijot.457

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…More recently, there has been dramatic progress in our formal understanding of nonequilibrium statistical physics and its relation to information processing, in general [61,62,[64][65][66][67][68][69][70][71][72][73][74][75][76][77][78].…”

Section: (A) Formalizing and Generalizing Landauer's Boundmentioning

confidence: 99%

The thermodynamic efficiency of computations made in cells across the range of life

Kempes

Wolpert

Cohen

et al. 2017

Phil. Trans. R. Soc. A.

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Biological organisms must perform computation as they grow, reproduce, and evolve. Moreover, ever since Landauer's bound was proposed it has been known that all computation has some thermodynamic cost -and that the same computation can be achieved with greater or smaller thermodynamic cost depending on how it is implemented. Accordingly an important issue concerning the evolution of life is assessing the thermodynamic efficiency of the computations performed by organisms. This issue is interesting both from the perspective of how close life has come to maximally efficient computation (presumably under the pressure of natural selection), and from the practical perspective of what efficiencies we might hope that engineered biological computers might achieve, especially in comparison with current computational systems. Here we show that the computational efficiency of translation, defined as free energy expended per amino acid operation, outperforms the best supercomputers by several orders of magnitude, and is only about an order of magnitude worse than the Landauer bound. However this efficiency depends strongly on the size and architecture of the cell in question. In particular, we show that the useful efficiency of an amino acid operation, defined as the bulk energy per amino acid polymerization, decreases for increasing bacterial size and converges to the polymerization 1 arXiv:1706.05043v1 [q-bio.OT] 15 Jun 2017 cost of the ribosome. This cost of the largest bacteria does not change in cells as we progress through the major evolutionary shifts to both single and multicellular eukaryotes. However, the rates of total computation per unit mass are nonmonotonic in bacteria with increasing cell size, and also change across different biological architectures including the shift from unicellular to multicellular eukaryotes.

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Section: (A) Formalizing and Generalizing Landauer's Boundmentioning

confidence: 99%

The thermodynamic efficiency of computations made in cells across the range of life

Kempes

Wolpert

Cohen

et al. 2017

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

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“…The past few decades have seen great advances in nonequilibrium statistical physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], resulting in many novel predictions and experiments [17][18][19]. Some of the most important results of this research have been powerful new tools for analyzing the dissipated work (or 'dissipation' for short) in nonequilibrium processes.…”

Section: Introductionmentioning

confidence: 99%

Dependence of dissipation on the initial distribution over states

Kolchinsky¹,

Wolpert²

2017

J. Stat. Mech.

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We analyze how the amount of work dissipated by a fixed nonequilibrium process depends on the initial distribution over states. Specifically, we compare the amount of dissipation when the process is used with some specified initial distribution to the minimal amount of dissipation possible for any initial distribution. We show that the difference between those two amounts of dissipation is given by a simple information-theoretic function that depends only on the initial and final state distributions. Crucially, this difference is independent of the details of the process relating those distributions. We then consider how dissipation depends on the initial distribution for a 'computer', i.e., a nonequilibrium process whose dynamics over coarse-grained macrostates implement some desired input-output map. We show that our results still apply when stated in terms of distributions over the computer's coarse-grained macrostates. This can be viewed as a novel thermodynamic cost of computation, reflecting changes in the distribution over inputs rather than the logical dynamics of the computation.

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Una aproximación a la construcción de modelos matemáticos para la descripción de la naturaleza

2016

Rev. Acad. Colomb. Cienc. Ex. Fis. Nat.

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Artículo de posesión para el ingreso como miembro correspondiente a la Academia Colombiana de Ciencias Exactas, Físicas y Naturales el 6 de abril de 2016 ResumenSe presenta una descripción de la forma como se afronta el problema de la abstracción mental, necesaria para el desarrollo de un modelo matemático, capaz de describir los fenómenos que rigen el comportamiento de la dinámica de procesos naturales, ante perturbaciones externas al sistema. El objetivo de este trabajo es encontrar la ecuación de balance, partiendo desde la ecuación de Liouville clásica en la escala microscópica hasta las ecuaciones de balance a escala macroscópica o ecuaciones de Navier-Stokes. Dividiendo magnitudes físicas como la velocidad en dos partes, una de ellas relacionada con el valor promedio y la otra con el fluctuante, genera la posibilidad de saltar de un escala a otra y así reducir la complejidad. En el artículo también se menciona de manera resumida el hecho que la complejidad se construye a partir de unidades simples; de esta manera, los modelos se consideran una abstracción de la realidad en la que se le asigna una ecuación matemática en diferentes escalas, tanto temporal como espacial, para explicar cómo la naturaleza se comporta y cómo ella se moldea para lograr sus determinadas formas. © Acad. Colomb. Cienc. Ex. Fis. Nat. 2016.Palabras clave: modelamiento, multi-escala, ecuaciones de balance. An approximation to setting up mathematical models for nature description AbtractA description of how everyone does abstractions to develop a mathematical model is presented; as well as the ability to describe the behaviour of nature processes dynamic when there are external perturbations. The aim of this work is to find the balance equation, starting from the classical Liouville equation on the microscopic scale until the balance equations on a macroscopic scale or Navier-Stokes equations. By dividing physical quantities such as velocity in two parts, one of which related to the average value and the other one with the fluctuation; it is possible to jump from one scale to another and reduces complexity. At this point, the complexity is constructed from simple units; therefore, the models are considered reality abstractions based on a mathematical equation formulated at different levels, both on time and space; as consequence, nature takes its shape due to the external influence, without forget the nature laws, by modifying the shape, adapting and looking for the less energy demand. © Acad. Colomb. Cienc. Ex. Fis. Nat. 2016. Key words:Modelling, mult-scale, balance equations. IntroducciónLa importancia de desarrollar modelos se relaciona con la dificultad de entender y explicar fenómenos desde el punto de vista experimental, con la imposibilidad de operar el sistema real en regiones de riesgo, y con tiempos de ensayo demasiado largos en los sistemas reales (días o meses); versus el corto tiempo de solución del modelo (segundos o minutos) en el computador que permite replicar la experimentación de fenómenos traslapados, predecir nuev...

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A Simple Derivation of Crooks Relation

Cited by 3 publications

References 18 publications

The thermodynamic efficiency of computations made in cells across the range of life

The thermodynamic efficiency of computations made in cells across the range of life

Dependence of dissipation on the initial distribution over states

Una aproximación a la construcción de modelos matemáticos para la descripción de la naturaleza

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