Current fluctuations in periodically driven systems

Barato, Andre C.; Chétrite, Raphaël

doi:10.1088/1742-5468/aabfc5

Cited by 55 publications

(93 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also prove our results for the case of a cyclic stochastic protocol [40,49,50]. Such protocols are convenient to perform illustrative calculations with specific models.…”

Section: Introductionsupporting

confidence: 57%

“…Such protocols are convenient to perform illustrative calculations with specific models. Furthermore, the proofs for stochastic protocols are a generalization of our results for deterministic protocols, since current fluctuations for a stochastic protocol with an infinitely large number of jumps are equivalent to current fluctuations for a deterministic protocol [50].…”

Section: Introductionmentioning

confidence: 76%

“…If a parabola bounds a ( ) I x from above then a corresponding parabola, which can be determined from equation (14), bounds λ α (z) from below. For illustrations of our results we perform calculations of λ α (z) using known methods [40,50].…”

Section: Large Deviationsmentioning

confidence: 99%

“…We also consider the case of an external protocol that is stochastic [40,49,50]. In order to mimic a deterministic periodic protocol, this stochastic protocol is cyclic and has N states.…”

Section: Stochastic Protocolmentioning

confidence: 99%

“…Consider a deterministic periodic protocol characterized by the rates w ij (t) and the period τ. If the rates of the model with a stochastic protocol are t = = ( ) w w t n N ij n ij and γ=N/τ, then in the limit of  ¥ N , current fluctuations for the stochastic protocol become equal to current fluctuations for the deterministic protocol [50]. Hence, the deterministic protocol corresponds to an asymptotic limit of a stochastic protocol.…”

Section: Stochastic Protocolmentioning

confidence: 99%

See 4 more Smart Citations

Bounds on current fluctuations in periodically driven systems

et al. 2018

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…We also prove our results for the case of a cyclic stochastic protocol [40,49,50]. Such protocols are convenient to perform illustrative calculations with specific models.…”

Section: Introductionsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 76%

Section: Large Deviationsmentioning

confidence: 99%

“…We also consider the case of an external protocol that is stochastic [40,49,50]. In order to mimic a deterministic periodic protocol, this stochastic protocol is cyclic and has N states.…”

Section: Stochastic Protocolmentioning

confidence: 99%

Section: Stochastic Protocolmentioning

confidence: 99%

See 3 more Smart Citations

Bounds on current fluctuations in periodically driven systems

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

Strong current response to slow modulation: A metabolic case-study

Forastiere

Falasco

Esposito

2020

The Journal of Chemical Physics

View full text Add to dashboard Cite

We study the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under timevarying metabolic conditions, modeled by a periodic modulation of the product concentration. We find that the system exhibits a strong nonlinear response to small driving frequencies both for the mean time-averaged current and for the fluctuations. For the first, we obtain an analytic formula by coarse-graining the original model to a solvable one. The result is nonperturbative in the modulation amplitude and frequency. We then refine the picture by studying the stochastic dynamics of the full system using a large deviations approach, that allows to show the resonant effect at the level of the time-averaged variance and signal-to-noise ratio. Finally, we discuss how this nonequilibrium effect may play a role in metabolic and synthetic networks.

show abstract

Computing time-periodic steady-state currents via the time evolution of tensor network states

Strand

Vroylandt

Gingrich

2022

The Journal of Chemical Physics

View full text Add to dashboard Cite

We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group (DMRG) algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Though trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial.

show abstract

Current fluctuations in periodically driven systems

Cited by 55 publications

References 39 publications

Bounds on current fluctuations in periodically driven systems

Bounds on current fluctuations in periodically driven systems

Strong current response to slow modulation: A metabolic case-study

Computing time-periodic steady-state currents via the time evolution of tensor network states

Contact Info

Product

Resources

About