We present thermoelectric power and resistivity measurements in the ferromagnetic superconductor URhGe for magnetic field applied along the hard magnetization b axis of the orthorhombic crystal. Reentrant superconductivity is observed near the the spin reorientation transition at $H_{R}$=12.75 T, where a first order transition from the ferromagnetic to the polarized paramagnetic state occurs. Special focus is given to the longitudinal configuration, where both electric and heat current are parallel to the applied field. The validity of the Fermi-liquid $T^2$ dependence of the resistivity through $H_R$ demonstrates clearly that no quantum critical point occurs at $H_R$. Thus the ferromagnetic transition line at $H_R$ becomes first order implying the existence of a tricritical point at finite temperature. The enhancement of magnetic fluctuations in the vicinity of the tricritical point stimulates the reentrance of superconductivity. The abrupt sign change observed in the thermoelectric power with the thermal gradient applied along the b axis together with the strong anomalies in the other directions is a definitive macroscopic evidence that in addition a significant change of the Fermi surface appears through $H_R$.
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