Fluctuation theorem for heat transport probed by a thermal 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.

16 pages, 7 figures

References in corpus (20)

• The large deviation approach to statistical mechanics
• Optimal energy quanta to current conversion
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Powerful and efficient energy harvester with resonant-tunneling quantum dots
• Strong bounds on Onsager coefficients and efficiency for three terminal thermoelectric transport in a magnetic field
• Scattering theory of nonlinear thermoelectric transport
• Inelastic Interaction Corrections and Universal Relations for Full Counting Statistics
• Full-counting statistics for molecular junctions: Fluctuation theorem and singularities
• Voltage and dephasing probes: a full counting statistics discussion
• Heat transport through a Josephson junction
• Fluctuation Theorem and Microreversibility in a Quantum Coherent Conductor
• Transient fluctuation relations for time-dependent particle transport
• Fluctuation Relations for Spintronics
• Magnetoasymmetric transport in a mesoscopic interferometer: From the weak to the strong coupling regime
• Magnetoasymmetric current fluctuations of single-electron tunneling
• Fluctuation relations and rare realizations of transport observables
• Current-voltage correlations in interferometers
• Giant current fluctuations in an overheated single electron transistor
• Work fluctuation theorem for a classical circuit coupled to a quantum conductor

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• Full counting statistics of the currents through a Kitaev chain and the exchange fluctuation theorem
• Statistics of energy dissipation in a quantum dot operating in the cotunneling regime