Classical Nernst engine

Abstract

We introduce a simple model for an engine based on the Nernst effect. In the presence of a magnetic field, a vertical heat current can drive a horizontal particle current against a chemical potential. For a microscopic model invoking classical particle trajectories subject to the Lorentz force, we prove a universal bound 3 − 2 √ 2 ≃ 0.172 for the ratio between maximum efficiency and Carnot efficiency. This bound, as the slightly lower one 1/6 for efficiency at maximum power, can indeed be saturated for large magnetic field and small fugacity irrespective of the aspect ratio.PACS numbers: 05.60. Cd, 05.70.Ln, Introduction.-The Nernst effect describes the emergence of an electrical voltage perpendicular to a heat current transversing an isotropic conductor in the presence of a constant magnetic field [1]. However, while Seebeck-based devices, for which the heat and the particle current are coupled without a magnetic field, have been the subject of intensive research efforts during the last decades [2][3][4][5], only a few attempts were made to utilize the Nernst effect for power generation [6][7][8][9]. This lack of interest may have been caused by the uncompetitive net efficiency of Nernst-based devices, which is inevitably suppressed by the energetic cost of the strong magnetic fields they require. New discoveries in the phenomenological theory of thermoelectric effects as well as recent experiments showing the accessibility of magnetic field effects in nanostructures even at low and moderate field strengths [10-13], however, cast new light on the topic of Nernst engines.Benenti and co-workers showed by a quite general analysis within the framework of linear irreversible thermodynamics that breaking the microscopic time-reversal symmetry by a magnetic field could, in principle, increase thermoelectric efficiency such that even devices operating reversibly at finite power seem to be achievable [14]. Such an intriguing suggestion asks for a better understanding of coupled heat and particle transport in magnetic fields. First progress in this direction was recently achieved within the paradigmatic class of multi-terminal models, for which it turned out that current conservation implies much stronger bounds on the efficiency than the standard rules of linear irreversible thermodynamics [15, 16]. For the minimal case of three terminals, these bounds were even shown to be tight [17]. Since these models were based on general particle transmission probabilities without reference to any specific microscopic dynamics, they leave the necessary conditions for saturating these bounds open.Simple mechanical models have led to remarkable insight into the microscopic mechanisms underlying heat and matter transport [18, 19], especially in the context of thermoelectric efficiency [20][21][22]. So far, the effect of a

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“…The same effect could be achieved with non-interacting conductors in magnetic fields, via a Nernst effect [59,60]. Note that Refs.…”

“…Note that Refs. [59,60] assumed that the reservoirs that carry the charge current (reservoirs L and R in our Fig. 1) are at temperatures chosen such that there is no heat flow out of them.…”