Free diffusion bounds the precision of currents in underdamped dynamics

Fischer, Lukas P.; Chun, Hyun-Myung; Seifert, Udo

doi:10.1103/physreve.102.012120

Cited by 30 publications

(33 citation statements)

References 37 publications

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“…(b)Uncertainty product as a function of the length t of the time window. The bound conjectured in Ref [15]. (dashed line) corresponds to free diffusion in y (κ = 0, dark grey).…”

mentioning

confidence: 84%

“…Violations of the TUR have been observed where time-reversal symmetry is broken through the presence of an external magnetic field [13,14]. It has also been shown that the ballistic motion on short timescales spoils the finite-time variant of the TUR, replacing it by a conjectured time-dependent bound that recovers the original TUR in the long-time limit [15].…”

mentioning

confidence: 99%

“…In Ref. [15], it had been conjectured that free diffusion sets a lower bound on the uncertainty product [the left hand side of the TUR (1)] for underdamped dynamics on finite time scales. While this supposed bound holds true for most generic potential landscapes (and in particular for uncoupled dynamics, e.g., a washboard potential in y-direction independent of x), it is broken for our design of an escapement.…”

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confidence: 99%

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Classical pendulum clocks break the thermodynamic uncertainty relation

Pietzonka

2021

Preprint

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A mechanical clock, such as a pendulum clock, uses an escapement to couple the motion of an oscillator to regulate the motion of another degree of freedom (a "hand") driven by an external force. Clocks built after this principle can yield high precision at low energetic cost. They provide a counterexample to the thermodynamic uncertainty relation, which is thus shown not to hold for systems undergoing driven Brownian diffusion with inertia. Considering a thermodynamically consistent, discrete model for an escapement mechanism, we first show that the oscillations of an underdamped harmonic oscillator in thermal equilibrium are sufficient to break the thermodynamic uncertainty relation. We then show that this is also the case in simulations of a fully continuous underdamped system with a potential landscape that mimics an escaped pendulum.

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“…(b)Uncertainty product as a function of the length t of the time window. The bound conjectured in Ref [15]. (dashed line) corresponds to free diffusion in y (κ = 0, dark grey).…”

mentioning

confidence: 84%

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confidence: 99%

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confidence: 99%

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Classical pendulum clocks break the thermodynamic uncertainty relation

Pietzonka

2021

Preprint

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“…First, we determine the leading order of the total entropy production rate by inserting eqs. (38) and ( 42) into eq. ( 35), which yields σ(T , v) = 1 t sys σ (0) (T , v) + O ( f /t sys ) ≡ 1 t sys τ f τ f 0…”

Section: Appendix a Diffusion Coefficients And Correlation Functionsmentioning

confidence: 99%

Thermodynamic Uncertainty Relation for Time-Dependent Driving

2020

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The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.

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“…More recently, the universal bound of TUR has been used to infer the dissipation rate from the fluctuating currents of dynamical processes [24]. The originally proposed relation has been extended to broader range of nonequilibrium processes [5,6,[25][26][27][28][29][30], including those generated in underdamped conditions [31], under periodic drives [8,32], and driven by velocity-dependent forces [33,34]. However, these processes are featured with the bounds less tight than that of the original TUR.…”

Section: Introductionmentioning

confidence: 99%

The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

Singh,

Hyeon

2021

Preprint

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Free diffusion bounds the precision of currents in underdamped dynamics

Cited by 30 publications

References 37 publications

Classical pendulum clocks break the thermodynamic uncertainty relation

Classical pendulum clocks break the thermodynamic uncertainty relation

Thermodynamic Uncertainty Relation for Time-Dependent Driving

The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

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