Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime

Abstract

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriate in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-Büttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry. These results demonstrate how quantum mechanics constraints thermodynamics.

8 pages, 3 figures, close to publish version

References in corpus (19)

• Thermoelectric energy harvesting with quantum dots
• Quantum limit of heat flow across a single electronic channel
• Optimal energy quanta to current conversion
• Strong bounds on Onsager coefficients and efficiency for three terminal thermoelectric transport in a magnetic field
• Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output
• Scattering theory of nonlinear thermoelectric transport
• Chiral thermoelectrics with quantum Hall edge states
• Thermoelectric efficiency of three-terminal quantum thermal machines
• Single-electron heat diode
• Efficiency of three-terminal thermoelectric transport under broken-time reversal symmetry
• Thermodynamic and quantum bounds on nonlinear DC thermoelectric transport
• Enhanced performance of joint cooling and energy production
• Bound on Thermoelectric Power in a Magnetic Field within Linear Response
• Quantum Nernst engines
• Mixed, charge and heat noises in thermoelectric nanosystems
• Conservation Laws and Thermodynamic Efficiencies
• Heat asymmetries in nanoscale conductors: The role of decoherence and inelasticity
• Universal electric current of interacting resonant-level models with asymmetric interactions: An extension of the Landauer formula
• Thermodynamics of Mesoscopic Quantum Systems

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