Discrete-time thermodynamic uncertainty relation

Proesmans, Karel; Broeck, C. Van den

doi:10.1209/0295-5075/119/20001

Cited by 205 publications

(262 citation statements)

References 37 publications

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“…Our trade-off relations do not imply the generalization of the thermodynamic uncertainty relation from [29] for the case of periodic protocols that are symmetric, i.e., t t…”

Section: Trade-off Between Speed and Precisionmentioning

confidence: 78%

“…A key feature of this parabolic bound is that it depends solely on the average entropy production and the average current, i.e., knowledge of the average entropy production and the average current implies a bound on arbitrary fluctuations of any thermodynamic current. There has been much recent work related to this universal principle about current fluctuations [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, the parabolic bound from [14,15] that depends on the average rate of entropy production does not apply to periodically driven systems. For the particular case of a timesymmetric protocol, a derivation of a thermodynamic uncertainty relation has been proposed in [29]. The relation between these two classes of nonequilibrium systems is also relevant for the mapping of artificial molecular machines, which are often driven by an external periodic protocol (see [41] for a counter-example), onto biological molecular motors, which are autonomous machines driven by ATP, as discussed in [42,43].…”

Section: Introductionmentioning

confidence: 99%

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Bounds on current fluctuations in periodically driven systems

et al. 2018

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Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem. More recently, it has been found that, for nonequilibrium stationary states, the full spectrum of fluctuations of any thermodynamic current is bounded by the average rate of entropy production and the average current. However, this bound does not apply to periodically driven systems, such as heat engines driven by periodic variation of the temperature and artificial molecular pumps driven by an external protocol. We obtain a universal bound on current fluctuations for periodically driven systems. This bound is a generalization of the known bound for stationary states. In general, the average rate that bounds fluctuations in periodically driven systems is different from the rate of entropy production. We also obtain a local bound on fluctuations that leads to a trade-off relation between speed and precision in periodically driven systems, which constitutes a generalization to periodically driven systems of the so called thermodynamic uncertainty relation. From a technical perspective, our results are obtained with the use of a recently developed theory for 2.5 large deviations for Markov jump processes with time-periodic transition rates.

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“…Our trade-off relations do not imply the generalization of the thermodynamic uncertainty relation from [29] for the case of periodic protocols that are symmetric, i.e., t t…”

Section: Trade-off Between Speed and Precisionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bounds on current fluctuations in periodically driven systems

et al. 2018

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“…The smaller the value of Q, the more regular and predictable is the trajectory generated from the process, rendering the output observable more precise. The proof and physical significance of this inequality have been discussed [5][6][7][8][9][10]. In the presence of large fluctuations inherent to cellular processes, harnessing energy into precise motion is critical for accuracy in cellular computation.…”

mentioning

confidence: 99%

Energetic costs, precision, and efficiency of a biological motor in cargo transport

Hwang

Hyeon

2017

Preprint

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Molecular motors play key roles in organizing the interior of cells. An efficient motor in cargo transport would travel with a high speed and a minimal error in transport time (or distance) while consuming minimal amount of energy. The travel distance and its variance of motor are, however, physically constrained by energy consumption, the principle of which has recently been formulated into the thermodynamic uncertainty relation. Here, we reinterpret the uncertainty measure (Q) defined in the thermodynamic uncertainty relation such that a motor efficient in cargo transport is characterized with a small Q. Analyses on the motility data from several types of molecular motors show that Q is a nonmonotic function of ATP concentration and load (f ). For kinesin-1, Q is locally minimized at [ATP] ≈ 200 µM and f ≈ 4 pN. Remarkably, for the mutant with a longer neck-linker this local minimum vanishes, and the energetic cost to achieve the same precision as the wild-type increases significantly, which underscores the importance of molecular structure in transport properties. For the biological motors studied here, their value of Q is semi-optimized under the cellular condition ([ATP] ≈ 1 mM, f = 0 − 1 pN). We find that among the motors, kinesin-1 at single molecule level is the most efficient in cargo transport.Biological systems are in nonequilibrium steady states (NESS) in which the energy and material currents flow constantly in and out of the system. Subjected to incessant thermal and nonequilibrium fluctuations, cellular processes are inherently stochastic and error-prone. To minimize detrimentaion effects, cells are equipped with a plethora of energy-consuming error-correction mechanisms. Trade-off relations between the energetic cost and information processing are ubiquitous in cellular processes, and have been a recurring theme in biology for many decades [1? ? -4].A recent study by Barato and Seifert [5] has formulated a concise inequality known as the thermodynamic uncertainty relation, the trade-off between energy consumption and precision of an observable from dissipative processes in NESS. To be more explicit, the uncertainty measure Q, defined as a product between the energy consumption (heat dissipation, Q(t)) from an energy-driven process in the steady state and the squared relative error of an output observable X(t), 2 X (t) = δX 2 / X 2 , is constant. It has been further conjectured that for an arbitrary chemical network formulated by Markov jump processes Q cannot be smaller than 2k B T ,The measure Q quantifies the uncertainty of a dynamic process. The smaller the value of Q, the more regular and predictable is the trajectory generated from the process, rendering the output observable more precise. The proof and physical significance of this inequality have been discussed [5][6][7][8][9][10]. In the presence of large fluctuations inherent to cellular processes, harnessing energy into precise motion is critical for accuracy in cellular computation.The uncertainty measure Q can be used to assess the e...

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“…It might be interesting to note that also thermodynamic properties like temperature T, Helmholtz energy F, chemical potential μ, volume V, and pressure Π do occur in these formulations. Indeed, the role of thermodynamic uncertainty relations as fundamental bounds in biological and chemical physics are currently under investigation [35][36][37]. It turns out that the bound C>0 can always be expressed in terms of the fundamental physical constants.…”

Section: Uncertainty Relationsmentioning

confidence: 99%

Conjecture of new inequalities for some selected thermophysical properties values

Hohm

2019

J. Phys. Commun.

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In 2005 it was rigorously shown with string theory methods that there is a lower bound for the ratio of the shear viscosity η and the volume density of entropy s=S/V given byHere we extend this result in a heuristic manner to other ratios of thermophysical properties. We conjectured that there are rigorous non-zero lower bounds for the Lorenz number L as well as other combinations of equilibrium and transport properties. We suggest that the lower bounds and the corresponding inequalities can be written in terms of the Planck units. We show that some of the proposed new inequalities set severe constraints on the behavior and properties of ordinary matter.

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Discrete-time thermodynamic uncertainty relation

Cited by 205 publications

References 37 publications

Bounds on current fluctuations in periodically driven systems

Bounds on current fluctuations in periodically driven systems

Energetic costs, precision, and efficiency of a biological motor in cargo transport

Conjecture of new inequalities for some selected thermophysical properties values

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