Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations

Abstract

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

Heat fluctuations and fluctuation theorems in the case of multiple reservoirs

“…By inspection we find the fundamental symmetry analogous to (2.16), 12) and from the spectral representation for the characteristic function, see Appendix A,…”

Statistics of heat exchange between two resistors

“…In contrast, for the experiments by Ciliberto et al [11,12] with T ∼ 100 K, R = 10 M , and l ∼ 1 cm one finds T /ω c ∼ 10 10 1, which corresponds to a strongly classical regime.…”

Thermal response of nonequilibriumRCcircuits

“…More details on the experimental set-up can be found in Ref. [34]. For the data used for the analysis discussed in the following section, the values of the components are: C = 100pF, C 1 = 680pF, C 2 = 420pF and R 1 = R 2 = 10MΩ.…”

“…For example, one could be interested in the response to temperature variations of a glassy system undergoing a relaxation process [32,33]. Alternatively, a nonequilibrium steady state may be imposed by putting the system in contact with two reservoirs at different temperatures [34,35]. It is the case of an experiment recently realized with a simple desktop electric circuit in which * baiesi@pd.infn.it † yolcu@pd.infn.it one resistor was kept at room temperature while the other was maintained at a lower temperature [34].…”

“…In this paper, we analyze the experiments of the thermally unbalanced electric circuit [34] and we discuss the good performances of a fluctuation-response relation [25,26] in computing the susceptibility of the system to a change of the colder, manipulable temperature. The primary goal of this work is to show how to apply this approach in practice.…”