A thermodynamic uncertainty relation for a system with memory

Terlizzi, Ivan Di; Baiesi, Marco

doi:10.1088/1751-8121/abbc7d

Cited by 12 publications

(11 citation statements)

References 54 publications

(99 reference statements)

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“…For generic protocols and initial Gaussian conditions, the quantities we computed for every time t ≥ 0 are the average particle position (19), its autocorrelation function (25) and hence its variance (27), the average work done on the system (36), its variance (38), and the entropy production rate (62). These formulas can be simplified in some standard scenarios, e.g.…”

Section: Discussionmentioning

confidence: 99%

“…In conclusion, we note that this framework yields average quantities but also their variances. Hence it is used [27] to derive one of the first examples of thermodynamic uncertainty relation [28][29][30][31][32][33][34][35] for systems with memory [36,37] .…”

Section: Discussionmentioning

confidence: 99%

“…Hence, Eqs. (27), (32) and (33) are the explicit expressions of the components of the covariance matrix.…”

Section: Variance Of the Position And Correlationsmentioning

confidence: 99%

“…As for the covariance matrix, we again use the expressions for the variance of position and velocity (27) and (32) alongside with their covariance (33), finding that…”

Section: Initial Conditions In the Infinite Pastmentioning

confidence: 99%

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Explicit Solution of the Generalised Langevin Equation

2020

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Generating an initial condition for a Langevin equation with memory is a non trivial issue. We introduce a generalisation of the Laplace transform as a useful tool for solving this problem, in which a limit procedure may send the extension of memory effects to arbitrary times in the past. This method allows us to compute average position, work, their variances and the entropy production rate of a particle dragged in a complex fluid by an harmonic potential, which could represent the effect of moving optical tweezers. For initial conditions in equilibrium we generalise the results by van Zon and Cohen, finding the variance of the work for generic protocols of the trap. In addition, we study a particle dragged for a long time captured in an optical trap with constant velocity in a steady state. Our formulas open the door to thermodynamic uncertainty relations in systems with memory.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Hence, Eqs. (27), (32) and (33) are the explicit expressions of the components of the covariance matrix.…”

Section: Variance Of the Position And Correlationsmentioning

confidence: 99%

“…As for the covariance matrix, we again use the expressions for the variance of position and velocity (27) and (32) alongside with their covariance (33), finding that…”

Section: Initial Conditions In the Infinite Pastmentioning

confidence: 99%

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Explicit Solution of the Generalised Langevin Equation

2020

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“…Although all these conditions are met by a colloidal heat engine operating in a complex fluid, to the best of our knowledge they have never been examined in the context of stochastic thermodynamic cycles. Therefore, it is of paramount importance to assess the role of viscoelasticity in the performance of this kind of engines, since the resulting frequency-dependent friction experienced by a colloidal particle can significantly impact the rate at which energy is dissipated into a viscoelastic bath [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Work Extraction and Performance of Colloidal Heat Engines in Viscoelastic Baths

Gomez-Solano

2021

Front. Phys.

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A colloidal particle embedded in a fluid can be used as a microscopic heat engine by means of a sequence of cyclic transformations imposed by an optical trap. We investigate a model for the operation of such kind of Brownian engines when the surrounding medium is viscoelastic, which endows the particle dynamics with memory friction. We analyze the effect of the relaxation time of the fluid on the performance of the colloidal engine under finite-time Stirling cycles. We find that, due to the frequency-dependence of the friction in viscoelastic fluids, the mean power delivered by the engine and its efficiency can be highly enhanced as compared to those in a viscous environment with the same zero-shear viscosity. In addition, with increasing fluid relaxation time the interval of cycle times at which positive power output can be delivered by the engine broadens. Our results reveal the importance of the transient behavior of the friction experienced by a Brownian heat engine in a complex fluid, which cannot be neglected when driven by thermodynamic cycles of finite duration.

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The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

Niggemann

Seifert

2021

J Stat Phys

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We investigate the thermodynamic uncertainty relation for the $$(1+1)$$ ( 1 + 1 ) dimensional Kardar–Parisi–Zhang (KPZ) equation on a finite spatial interval. In particular, we extend the results for small coupling strengths obtained previously to large values of the coupling parameter. It will be shown that, due to the scaling behavior of the KPZ equation, the thermodynamic uncertainty relation (TUR) product displays two distinct regimes which are separated by a critical value of an effective coupling parameter. The asymptotic behavior below and above the critical threshold is explored analytically. For small coupling, we determine this product perturbatively including the fourth order; for strong coupling we employ a dynamical renormalization group approach. Whereas the TUR product approaches a value of 5 in the weak coupling limit, it asymptotically displays a linear increase with the coupling parameter for strong couplings. The analytical results are then compared to direct numerical simulations of the KPZ equation showing convincing agreement.

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A thermodynamic uncertainty relation for a system with memory

Cited by 12 publications

References 54 publications

Explicit Solution of the Generalised Langevin Equation

Explicit Solution of the Generalised Langevin Equation

Work Extraction and Performance of Colloidal Heat Engines in Viscoelastic Baths

The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

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