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A problem of the definition of the heat transported in thermomagneticphenomena has been well realized in the late sixties, but not solved up todate. Ignoring this problem, numerous recent theories grossly overestimate thethermomagnetic coefficients in strongly interacting systems. Here we develop agauge-invariant microscopic approach, which shows that the heat transfer shouldinclude the energy of the interaction between electrons and a magnetic field.We also demonstrate that the surface currents induced by the magnetic fieldtransfer the charge in the Nernst effect, but do not transfer the heat in theEttingshausen effect. Only with these two modifications of the theory, thephysically measurable thermomagnetic coefficients satisfy the Onsager relation.We critically revised the Gaussian fluctuation model above the superconductingtransition and show that the gauge invariance uniquely relates thermomagneticphenomena in the Fermi liquid with the particle-hole asymmetry.

How Magnetic Field Enters Heat Current: Application to Fluctuation Nernst Effect