Fluctuation theorem for heat transport probed by a thermal probe electrode

Abstract

We analyze the full-counting statistics of the electric heat current flowing in a two-terminal quantum conductor whose temperature is probed by a third electrode ("probe electrode"). In particular we demonstrate that the cumulant-generating function obeys the fluctuation theorem in the presence of a constant magnetic field. The analysis is based on the scattering matrix of the three-terminal junction (comprising of the two electronic terminals and the probe electrode), and a separation of time scales: it is assumed that the rapid charge transfer across the conductor and the rapid relaxation of the electrons inside the probe electrode give rise to much slower energy fluctuations in the latter. This separation allows for a stochastic treatment of the probe dynamics, and the reduction of the three-terminal setup to an effective two-terminal one. Expressions for the lowest nonlinear transport coefficients, e.g., the linear-response heat-current noise and the second nonlinear thermal conductance, are obtained and explicitly shown to preserve the symmetry of the fluctuation theorem for the two-terminal conductor. The derivation of our expressions which is based on the transport coefficients of the three-terminal system explicitly satisfying the fluctuation theorem, requires the full calculations of vertex corrections.

Thermoelectric energy harvesting with quantum dots

“…The interest on electronic heat noise has appeared only very recently [108,109,110,111,112,113,114,115]. Already in the linear regime the chargeheat cross-correlations are related to Seebeck-like and Peltier-like coefficients by means of an extended three-terminal fluctuation-dissipation theorem.…”

Dynamics of energy transport and entropy production in ac-driven quantum electron systems

“…The foundations of this area were in part developed after the proposal of the Jarzynski's equality [17] and Crook's theorem [18] and a subsequent number of fluctuations relations [19][20][21][22][23][24][25][26][27][28][29][30]. Recently, linear response proposals in close relation to thermodynamics have been formulated for open quantum systems and quasiclassical systems under periodic driving [13,[31][32][33].…”

Fluctuation of heat current in Josephson junctions

“…8,9 When mesoscopic systems are considered, fluctuations in heat transport can lead to fluctuations in other quantities -such as the energy stored on a small metal island -and eventually, in more accessible observables, such as charge current [10][11][12] or temperature measured by a generic temperature probe. 13 In addition to the theoretical question on how the coherent physics of phase differences in superconducting order parameters manifest in statistical properties of heat transport, questions on fluctuations can also be of interest in systems that utilize mesoscopic superconductors in a nonequilibrium settings for example for radiation detection. 14 In this work, we find the statistics of temperature-driven quasiparticle heat transport in a Josephson junction of arbitrary transparency, as illustrated in Fig.…”