Tightening the uncertainty principle for stochastic currents

Polettini, Matteo; Lazarescu, Alexandre; Esposito, Massimiliano

doi:10.1103/physreve.94.052104

Cited by 131 publications

(142 citation statements)

References 34 publications

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“…As occurs with the analogous bounds on time-integrated currents [1][2][3][4], an immediate consequence of the bounds on the rate function or cumulant generating function are the thermodynamic uncertainty relations [13][14][15]. From Eq.…”

Section: Level 25 and Fluctuation Boundsmentioning

confidence: 99%

“…Just like in the case of integrated currents [13][14][15], where there is an unavoidable tradeoff between precision and dissipation, the uncertainty in the estimation of a counting observable is bounded generically by the overall average activity in the process.…”

Section: Level 25 and Fluctuation Boundsmentioning

confidence: 99%

“…Obtained by means Level 2.5 [5][6][7] dynamical large deviation methods [8][9][10][11][12], these results stipulate general lower bounds for fluctuations at any order of all empirical currents in the stationary state of a stochastic process [1][2][3][4]. A corollary are thermodynamic uncertainty relations [13][14][15] connecting the estimation error of time-integrated currents to overall dissipation.…”

Section: Introductionmentioning

confidence: 97%

“…[1][2][3][4] and [13][14][15][16][17][18] focus on trajectory observables asymmetric under time reversal, such as empirical currents, which can be positive or negative and can increase and decrease with time. Here we consider instead trajectory observables which are always non-negative and strictly nondecreasing with time.…”

Section: Introductionmentioning

confidence: 99%

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Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

2017

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Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision of estimation to average dissipation. Here we consider this problem but for counting observables, i.e., trajectory observables which, in contrast to currents, are non-negative and nondecreasing in time (and possibly symmetric under time reversal). In the steady state, their fluctuations to all orders are bound from below by a Conway-Maxwell-Poisson distribution dependent only on the averages of the observable and of the dynamical activity. We show how to obtain the corresponding bounds for first-passage times (times when a certain value of the counting variable is first reached) and their uncertainty relations. Just like entropy production does for currents, dynamical activity controls the bounds on fluctuations of counting observables.

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Section: Level 25 and Fluctuation Boundsmentioning

confidence: 99%

Section: Level 25 and Fluctuation Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

2017

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“…This effort has recently been followed by a general proof employing the large deviation theory [12][13][14]. * hyeoncb@kias.re.kr…”

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confidence: 99%

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

Hyeon

Hwang

2017

Phys. Rev. E

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Using Brownian motion in periodic potentials V (x) tilted by a force f , we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q, and in order to limit the output fluctuation within a relative uncertainty , at least 2kBT / 2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium (f V (x)) but also at far-from-equilibrium (f V (x)), more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particle is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a new bound of nonequilibrium fluctuations that the variance of dissipated heat (σ 2 q ) increases with its mean (µq) and cannot be smaller than 2kBT µq.Precise determination of an output information from a thermodynamically dissipative process necessarily incurs energetic cost to generate it. Trade-offs between energetic cost and information processing in biochemical and biomolecular processes have been highlighted for the last decades [1][2][3][4][5]. Among others, Barato and Seifert [1] have recently conjectured a fundamental bound in the minimal heat dissipation (q) to generate an output with relative uncertainty ( ). To be specific, when a molecular motor moves along cytoskeletal filament [6][7][8], the chemical free energy transduced into the motor movement, which results in a travel distance of the motor X(t), is eventually dissipated as heat into the surrounding media [9,10], the amount of which increases with the time ( q ∼ t). Because of the inherent stochasticity of chemical processes, the travel distance X(t) has its own variance σ 2 X = (δX(t)) 2 , and defines a time-dependent fluctuation in the output, whose squared quantity decreases with time t, as 2 X ∼ t −1 . The product of the two quantities, Q, is, in fact, independent of t [1, 11], and it was further argued that Q is always greater than 2k B T for any process that can be described as Markov jump process on a suitable network. This notion is concisely written asThe validity of this inequality was claimed for general Markovian networks [1,2], and was partly proved at near equilibrium, linear response regime [1]. This effort has recently been followed by a general proof employing the large deviation theory [12][13][14]. * hyeoncb@kias.re.krHere, while limited to a particular model, we provide a less abstract and physically more tangible proof of the thermodynamic uncertainty relation (Eq....

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Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

2018

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We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a nonlinear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

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Tightening the uncertainty principle for stochastic currents

Cited by 131 publications

References 34 publications

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

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