We report an experimental and theoretical analysis of the energy exchanged between two conductors kept at different temperature and coupled by the electric thermal noise. Experimentally we determine, as functions of the temperature difference, the heat flux, the out-of-equilibrium variance and a conservation law for the fluctuating entropy, which we justify theoretically. The system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. Our results set strong constrains on the energy exchanged between coupled nano-systems held at different temperatures.The fluctuations of thermodynamics variables play an important role in understanding the out-of-equilibrium dynamics of small systems [1, 2], such as Brownian particles [3][4][5][6][7], molecular motors [8] and other small devices [9]. The statistical properties of work, heat and entropy, have been analyzed, within the context of the fluctuation theorem [10] and stochastic thermodynamics [1, 2], in several experiments on systems in contact with a single heat bath and driven out-of-equilibrium by external forces or fields [3][4][5][6][7][8][9]. In contrast, the important case in which the system is driven out-of-equilibrium by a temperature difference and energy exchange is produced only by the thermal noise has been analyzed only theoretically on model systems [11][12][13][14][15][16][17][18][19] but never in an experiment because of the intrinsic difficulties of dealing with large temperature differences in small systems.We report here an experimental and theoretical analysis of the statistical properties of the energy exchanged between two conductors kept at different temperature and coupled by the electric thermal noise, as depicted in fig. 1a. This system is inspired by the proof developed by Nyquist [20] in order to give a theoretical explanation of the measurements of Johnson [21] on the thermal noise voltage in conductors. In his proof, assuming thermal equilibrium between the two conductors, he deduces the Nyquist noise spectral density. At that time, well before Fluctuation Dissipation Theorem (FDT), this was the second example, after the Einstein relation for Brownian motion, relating the dissipation of a system to the amplitude of the thermal noise. In this letter we analyze the consequences of removing the Nyquist's equilibrium conditions and we study the statistical properties of the energy exchanged between the two conductors kept at different temperature. This system is probably among the simplest examples where recent ideas of stochastic thermodynamics can be tested but in spite of its simplicity the explanation of the observations is far from trivial. We measure experimentally the heat flowing between the two heath baths, and show that the fluctuating entropy exhibits a conservation law. This system is very general because is ruled by the same equations of two Brownian particles kept at different temperatures and coupled by an elastic force [13,19]. Thus it gives more insight into t...

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With the improved design there is no need to control the total operation time t 0 , while the time dependence of the voltage and¯ux can be optimized such that the time span of the manipulations t is long enough to simplify time control and short enough to speed up the computation.Also, the circuit of the current source, with resistance R I , which couples the¯ux © x to the SQUID by the mutual inductance M, introduces¯uctuations and may destroy the coherence of the qubit dynamics. At the degeneracy point, the decoherence time is 21,22 t I 1=p 3 R I =R K © 2 0 =E 0 J M 2 ~=k B T. This dephasing is slow if

We study both experimentally and theoretically the statistical properties of the energy exchanged between two electrical conductors, kept at different temperature by two different heat reservoirs, and coupled by the electric thermal noise. Such a system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. We measure the heat flowing between the two reservoirs, the thermodynamic work done by one part of the system on the other, and we show that these quantities exhibit a long time fluctuation theorem. Furthermore, we evaluate the fluctuating entropy, which satisfies a conservation law. These experimental results are fully justified by the theoretically analysis. Our results give more insight into the energy transfer in the famous Feymann ratchet widely studied theoretically but never in an experiment. 05.70.Ln

We present a detailed analysis of the energy dissipation averaged over a distance r,⑀ r , in terms of a stochastic process through scales. Using experimental data recorded in a low temperature helium jet, we give evidence that the probability density function of ln(⑀ r) obeys a Fokker-Planck equation. The drift and diffusion coefficients are calculated directly from the data. The drift is linear in ln(⑀ r) and the diffusion is constant. With these coefficients, the equation can be solved exactly, giving a Gaussian probability density function for ln(⑀ r). The mean and variance of this quantity are discussed in comparison with other log-normal models of intermittency. ͓S1063-651X͑97͒12911-7͔

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This article reports on an experimental study of the fluctuations of energy flux between a granular gas and a small driven harmonic oscillator. The DC-motor driving this system is used simultaneously as actuator and probe. The statistics of work fluctuations at controlled forcing, between the motor and the gas are examined from the viewpoint of the Fluctuation Theorem. A characteristic energy Ec of the granular gas, is obtained from this relation between the probabilities of an event and its reversal.

International audienceRecently, Friedrich and Peinke demonstrated empirically that a Fokker–Planck equation describesthe scale dependence of probability distribution functions of longitudinal velocity increments vr infully developed turbulent flows. Thanks to the analysis of an experimental velocity signal, thestochastic process vr is further investigated by examining the related Langevin equation. Thisprocess is found to be Markovian in scale because the turbulent velocity field is correlated overdistances much larger than the correlation length r of its spatial derivative. A Gaussianapproximation for the random force yields evolution equations for the structure functions ^vrn&.Analytic solutions are obtained, in agreement with experimental data for even-order moments whenthe scale r is larger than a few times r. The third-order moment ^vr3& is found linear in r, as predictedby Kolmogorov’s four-fifths law