Heat fluctuations and fluctuation theorems in the case of multiple reservoirs

Abstract

We consider heat fluctuations and fluctuation theorems for systems driven by multiple reservoirs. We establish a fundamental symmetry obeyed by the joint probability distribution for the heat transfers and system coordinates. The symmetry leads to a generalisation of the asymptotic fluctuation theorem for large deviations at large times. As a result the presence of multiple reservoirs influence the tails in the heat distribution. The symmetry, moreover, allows for a simple derivation of a recent exact fluctuation theorem valid at all times. Including a time dependent work protocol we also present a derivation of the integral fluctuation theorem.

Theoretical description of effective heat transfer between two viscously coupled beads

“…In particular, the last property had been previously predicted only for systems with a conservative coupling [13] and we have proved it also in the case of dissipative linear coupling. For all the theoretical predictions, the experimental results show a very good agreement.…”

“…Following the protocol discussed in [13,21], we now assume that we prepare our system such that at t → −∞ the temperature difference is vanishing ∆T = 0, and then at t = 0 we suddenly turn on the temperature difference ∆T , with T 1 = T + ∆T , and start measuring the heat currents for t ≥ 0. We assume to prepare the system in the same way along the backward trajectories: at t = τ − t → −∞ we take ∆T = 0, and then at t = 0 we "turn on" the temperature difference ∆T and start measuring the heat currents along the backward trajectories.…”

“…The heat transfer between two reservoirs kept at different temperatures, is certainly the simplest and probably the most fundamental out-of-equilibrium phenomenon that one can study. However, in small systems where the effects of thermal fluctuations on the mean heat flux cannot be neglected, this situation has been analyzed mainly in theoretical models [2][3][4][5][6][7][8][9][10][11][12][13]. Only a few very recent experiments have studied heat flux fluctuations [1,[14][15][16], because of the intrinsic difficulties of dealing with large temperature differences at small scales.…”

“…Motivated by our previous experimental findings, in this article we derive the Fluctuation Theorems (FTs) characterizing the "effective heat" transfer between two Brownian particles interacting with non-conservative linear forces, both in the transient and stationary regime. This is an important problem in the study of the thermodynamics of small motors and Brownian ratchets, because fluctuating energy fluxes have been mostly investigated in systems with conservative couplings [5][6][7][11][12][13], and their statistical properties for dissipative interactions have been less discussed. For example they were addressed in ref.…”

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

“…However, low-dimensional systems in contact with different energy or particle baths represent an excellent test-bed for some of the most recent ideas in classical and quantum out-ofequilibrium statistical physics [1]. For example, one can show that a chain of quantum harmonic oscillators in contact with two heat baths at different temperatures exhibits a steady state fluctuation theorem, setting constraints on the entropy production [9], in all respects equivalent to the fluctuation theorem for the corresponding classical case [10]. Furthermore, chains of oscillators have been used as model systems to study heat conduction in solids, in particular to test the validity of Fourier law, according to which the heat current across a material subject to a temperature gradient scales as the inverse of the system size [1].…”