Theoretical description of effective heat transfer between two viscously coupled beads

Bérut, Antoine; Imparato, Alberto; Petrosyan, Artyom; Ciliberto, S.

doi:10.1103/physreve.94.052148

Cited by 18 publications

(30 citation statements)

References 33 publications

(64 reference statements)

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“…We derive exact asymmetry relations, characterizing the state of the system, for the two-dimensional as well as for the one-dimensional projected dynamics, revealing a peculiar behavior for the corresponding effective "temperatures". The functional form of the latter appears perhaps to be even more striking than the one obtained for the exchanged heat in transient and stationary regimes [8]. Moreover, our relations are more detailed than standard ones, because they concern instantaneous values, rather than averaged values of the observables of interest.…”

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confidence: 73%

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Asymmetry relations and effective temperatures for biased Brownian gyrators

et al. 2018

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We focus on a paradigmatic two-dimensional model of a nanoscale heat engine, -the so-called Brownian gyrator -whose stochastic dynamics is described by a pair of coupled Langevin equations with different temperature noise terms. This model is known to produce a curl-carrying non-equilibrium steady-state with persistent angular rotations. We generalize the original model introducing constant forces doing work on the gyrator, for which we derive exact asymmetry relations, that are reminiscent of the standard fluctuation relations. Unlike the latter, our relations concern instantaneous and not time averaged values of the observables of interest. We investigate the full two-dimensional dynamics as well as the dynamics projected on the x-and y-axes, so that information about the state of the system can be obtained from just a part of its degrees of freedom. Such a state is characterized by effective "temperatures" that can be measured in nanoscale devices, but do not have a thermodynamic nature. Remarkably, the effective temperatures appearing in full dynamics are distinctly different from the ones emerging in its projections, confirming that they are not thermodynamic quantities, although they precisely characterize the state of the system. While in the past statistical physics has been mainly devoted to the microscopic basis of the macroscopic behaviour, present day research is largely addressing "small" or non-thermodynamic systems, which either evolve spontaneously or are subjected to external drivings and constraints. Unlike macroscopic systems, that are by and large described by thermodynamics and linear response theory, these systems are still hard to be framed within a comprehensive theory.In fact, macroscopic observations amount to drastic projections from highly dimensional spaces to spaces of observables that consist of just a few dimensions. This is the reason why thermodynamics is so universal; those projections loose an enormous amount of information about the microscopic dynamics, hence the properties of observables only minimally depend on such microscopic details, provided a few conditions are met. Basically, it suffices that atomic forces are short ranged and repulsive. Then, universality as well as the equivalence of ensembles are established, and the resulting theory of macroscopic objects very generally holds. On the contrary, the behavior of systems made of a non-thermodynamic number of elementary constituents strongly depends on all defining parameters, and a theory as widely applicable as thermodynamics can hardly be envisaged.Nevertheless, one common facet of such systems is that their observables undergo non-negligible fluctuations. Therefore, the seminal paper [1] represents a pioneering attempt towards a unified theory of fluctuating phenomena [2,3]. Its chief result is called Fluctuation Relation (FR), and it constitutes one of the first exact results obtained for systems which are almost arbitrarily far from equilibrium. Close to equilibrium the FR reproduces the Green-Kubo and Onsager re...

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confidence: 73%

“…In Ref. [8] this analysis was extended to obtain both transient and steady states fluctuation relations, that respectively hold for all and only for asymptotic observation time intervals, in accord with our discussion above. An experimental realization of gyrators was developed also in Ref.…”

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confidence: 82%

Asymmetry relations and effective temperatures for biased Brownian gyrators

et al. 2018

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“…Thus, this experiment clearly establishes a relationship between the mean and the variance of the entropy production rate in a system driven out of equilibrium by the temperature difference between two thermal baths coupled by electrical noise. Because of the formal analogy with Brownian motion, the results also apply to mechanical coupling [95,97,98].…”

Section: Entropy Production Ratementioning

confidence: 99%

Experiments in Stochastic Thermodynamics: Short History and Perspectives

2017

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We summarize in this article the experiments which have been performed to test the theoretical findings in stochastic thermodynamics such as fluctuation theorem, Jarzynski equality, stochastic entropy, out-ofequilibrium fluctuation dissipation theorem, and the generalized first and second laws. We briefly describe experiments on mechanical oscillators, colloids, biological systems, and electric circuits in which the statistical properties of out-of-equilibrium fluctuations have been measured and characterized using the abovementioned tools. We discuss the main findings and drawbacks. Special emphasis is given to the connection between information and thermodynamics. The perspectives and followup of stochastic thermodynamics in future experiments and in practical applications are also discussed.

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“…In the context of classical stochastic thermodynamics, experiments where a single particle is constrained on periodic circular tracks have been performed, e.g, in [40] where a 3D toroidal laser trap was used to force a colloidal particle to perform circular trajectories along a periodic potential. Brownian systems with 2 degrees of freedom, where the local temperature can be controlled, have been studied, for example, in [41][42][43][44].…”

Section: Discussionmentioning

confidence: 99%

Quantum duets working as autonomous thermal motors

Drewsen

Imparato

2019

Phys. Rev. E

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We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a non-vanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and characterize its steady state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of refs. [1, 2] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the non-linear, non-equilibrium regime.

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Theoretical description of effective heat transfer between two viscously coupled beads

Cited by 18 publications

References 33 publications

Asymmetry relations and effective temperatures for biased Brownian gyrators

Asymmetry relations and effective temperatures for biased Brownian gyrators

Experiments in Stochastic Thermodynamics: Short History and Perspectives

Quantum duets working as autonomous thermal motors

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