Thermodynamic cost of measurements

Granger, Léo; Kantz, Holger

doi:10.1103/physreve.84.061110

Cited by 45 publications

(77 citation statements)

References 32 publications

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“…The second law in equation (3) implies that the increase in the free energy given by equation (12) requires a work 25,43,56,57 W meas ≥ F (mem) meas + kTI (X , M)…”

Section: Cost Of Measurementmentioning

confidence: 99%

Thermodynamics of information

2015

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By its very nature, the second law of thermodynamics is probabilistic, in that its formulation requires a probabilistic description of the state of a system. This raises questions about the objectivity of the second law: does it depend, for example, on what we know about the system? For over a century, much e ort has been devoted to incorporating information into thermodynamics and assessing the entropic and energetic costs of manipulating information. More recently, this historically theoretical pursuit has become relevant in practical situations where information is manipulated at small scales, such as in molecular and cell biology, artificial nano-devices or quantum computation. Here we give an introduction to a novel theoretical framework for the thermodynamics of information based on stochastic thermodynamics and fluctuation theorems, review some recent experimental results, and present an overview of the state of the art in the field. S oon after the discovery of the second law of thermodynamics, James Clerk Maxwell illustrated the probabilistic nature of the law with a gedanken experiment, now known as Maxwell's demon 1,2 . He argued that if an intelligent being-a demon-had information about the velocities and positions of the particles in a gas, then that demon could transfer the fast, hot particles from a cold reservoir to a hot one, in apparent violation of the second law 1,2 .Maxwell's demon revealed the relationship between entropy and information for the first time-demonstrating that, by using information, one can relax the restrictions imposed by the second law on the energy exchanged between a system and its surroundings. But formulations of the second law attributed to Rudolf Clausius, Lord Kelvin and Max Planck 3 make no mention of information. Reconciling these two pictures involves two separate tasks. First, we must refine the second law to incorporate information explicitly. And second, we must clarify the physical nature of information, so that it enters the second law not as an abstraction, but as a physical entity. In this way, information manipulations such as measurement, erasure, copying and feedback can be thought of as physical operations with thermodynamic costs.The first task was partially accomplished by Léo Szilárd, who devised a stylized version of Maxwell's demon. Szilárd's demon exploits one bit of information (the outcome of an unbiased yes/no measurement) to implement a cyclic process that extracts kT ln 2 of energy as work from a thermal reservoir at temperature T , where k is Boltzmann's constant 4 . This suggests a quantitative relationship between the information used by the demon and the extractable work from a single thermal reservoir.Efforts to address the second task have been many and varied 1,2 . Léon Brillouin quantified the cost of measurement in some specific situations; Marian Smoluchowski 5 and Richard Feynman 6 demonstrated that fluctuations prevent apparent second-law violations in autonomous demons; and Rolf Landauer, Charles Bennett and Oliver Penrose 7 prov...

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“…The second law in equation (3) implies that the increase in the free energy given by equation (12) requires a work 25,43,56,57 W meas ≥ F (mem) meas + kTI (X , M)…”

Section: Cost Of Measurementmentioning

confidence: 99%

Thermodynamics of information

2015

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“…This division has been fruitful. Theoretical studies of memories, which have been verified by experiment [4], have led to insights into the thermodynamic costs of measurement [5] and erasure [6][7][8][9][10][11]; copying [12,13]; and proofreading [12]; while theoretical [14][15][16][17][18][19][20] and experimental [21,22] investigations of information (or feedback) motors have explored the fundamental limits to the conversion of information into work.Nevertheless, the thermodynamic qualities of information still need to be clarified, especially the mechanisms that allow a motor to exploit information to rectify thermal fluctuations. With this goal in mind, we highlight in this Letter the difference between information and a more traditional thermodynamic resource, the chemical free energy.…”

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confidence: 99%

“…, without affecting the ratchet, Z ′ = Z, though possibly changing the nonequilibrium free energy of the memory to F (M ′ ) = F (M ) [5,11].…”

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Imitating Chemical Motors with Optimal Information Motors

2013

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To induce transport, detailed balance must be broken. A common mechanism is to bias the dynamics with a thermodynamic fuel, such as chemical energy. An intriguing, alternative strategy is for a Maxwell demon to effect the bias using feedback. We demonstrate that these two different mechanisms lead to distinct thermodynamics by contrasting a chemical motor and information motor with identical dynamics. To clarify this difference, we study both models within one unified framework, highlighting the role of the interaction between the demon and the motor. This analysis elucidates the manner in which information is incorporated into a physical system. PACS numbers: 05.70. Ln, Information is physical [1]: it is stored in physical memories, and therefore the processing of information is constrained by the same thermodynamic limitations as any other physical process [2,3]. Remarkably, once information has been obtained, it can then serve as a thermodynamic resource similar to free energy. These observations have been the historic points of departure for investigations into the nature of information [2,3]. As a consequence, research has either focused on the manipulation of information in isolated memories, or simply on the engines that utilize that information. This division has been fruitful. Theoretical studies of memories, which have been verified by experiment [4], have led to insights into the thermodynamic costs of measurement [5] and erasure [6][7][8][9][10][11]; copying [12,13]; and proofreading [12]; while theoretical [14][15][16][17][18][19][20] and experimental [21,22] investigations of information (or feedback) motors have explored the fundamental limits to the conversion of information into work.Nevertheless, the thermodynamic qualities of information still need to be clarified, especially the mechanisms that allow a motor to exploit information to rectify thermal fluctuations. With this goal in mind, we highlight in this Letter the difference between information and a more traditional thermodynamic resource, the chemical free energy. We elaborate this distinction by comparing the entropy production rates of two motors with identical dynamics: a chemical motor powered by a chemical potential gradient and an information motor driven by feedback. For the chemical motor, we use traditional methods of thermodynamic analysis [23]. However, such methods cannot be applied to the information motor when the memory is left unspecified. Even still, a useful bound for its entropy production can be obtained from a refinement of the second law of thermodynamics for feedback and information, introduced by Sagawa and Ueda [11]. We demonstrate that, despite the identical dynamics, the information motor presents qualitatively different thermodynamics. We then trace this discrepancy to the features of the interaction between the ratchet and the memory by introducing a physical model of the information motor.Our motors are patterned on the Brownian ratchet [24] pictured in Fig. 1. The ratchet is composed of a particleFIG. 1. D...

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“…We begin by presenting a model for copying a single bit of information in the spirit of those proposed in [8,[16][17][18], see Fig. 1a.…”

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Kinetic versus Energetic Discrimination in Biological Copying

2013

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We study stochastic copying schemes in which discrimination between a right and a wrong match is achieved via different kinetic barriers or different binding energies of the two matches. We demonstrate that, in single-step reactions, the two discrimination mechanisms are strictly alternative and can not be mixed to further reduce the error fraction. Close to the lowest error limit, kinetic discrimination results in a diverging copying velocity and dissipation per copied bit. On the opposite, energetic discrimination reaches its lowest error limit in an adiabatic regime where dissipation and velocity vanish. By analyzing experimentally measured kinetic rates of two DNA polymerases, T7 and Polγ, we argue that one of them operates in the kinetic and the other in the energetic regime. Finally, we show how the two mechanisms can be combined in copying schemes implementing error correction through a proofreading pathway.PACS numbers: 87.10. Vg, 87.18.Tt, 05.70.Ln Living organisms need to process signals in a fast and reliable way. Copying information is a task of particular relevance, as it is required for the replication of the genetic code, the transcription of DNA into mRNA, and its translation into a protein. Reliability is fundamental, since errors can result in the costly (or harmful) production of a non-functional protein. Indeed, cells have developed mechanisms to reduce the copying error rate η to values as low as η ∼ 10 −4 for protein transcription-translation [1] and η ∼ 10 −10 for DNA replication [2]. Such mechanisms include multiple discrimination steps [1, 2] and pathways to undo wrong copies as in proofreading [2,[4][5][6] or backtracking [7].Biological information is copied by thermodynamic machines that operate at a finite temperature. There is agreement that this fact alone implies a lower limit on the error rate. However, contrasting results have been obtained regarding the nature of this limit. In particular, it is not clear when it is reached in a slow and quasi-adiabiatic regime, or in a fast and dissipative one. As clarified by Bennett [8], information can be copied adiabatically. Indeed, the copying scheme proposed in Hopfield's seminal proofreading paper [2] reaches its minimum error at zero velocity and zero dissipation [9]. In contrast, a copolymerization model proposed few years later by Bennett [1,11,12], achieves its minimum error in a highly dissipative regime, where velocity and dissipation diverge. Some of the biological literature has favoured that the minimum error is achieved in near-equilibrium conditions [9]. This view is however not unanimous [13]. Recent biophysical literature supports a dissipative minimum error limit [11,12,14,15]. Similar disagreements are also present in models including proofreading. The proofreading model in [1] dissipates systematically less than the corresponding copying, while in other models [2, 4], at low errors, dissipation comes mainly from the proofreading step.In this Letter, we show how these contrasting results can be rationalized noting that...

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Thermodynamic cost of measurements

Cited by 45 publications

References 32 publications

Thermodynamics of information

Thermodynamics of information

Imitating Chemical Motors with Optimal Information Motors

Kinetic versus Energetic Discrimination in Biological Copying

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