We report the thermoelectric transport properties in the orbital-ordered Mott insulating phase of Ca$_2$RuO$_4$ close to and far from equilibrium. Near equilibrium conditions where the temperature gradient is only applied to the sample, an insulating but non-monotonic temperature variation of the Seebeck coefficient is observed, which is accounted for in terms of a temperature-induced suppression of the orbital order. In non-equilibrium conditions where we have applied high electrical currents, we find that the Seebeck coefficient is anomalously increased in magnitude with increasing external current. The present result clearly demonstrates a non-thermal effect since the heating simply causes a decrease of the Seebeck coefficient, implying a non-trivial non-equilibrium effect such as a modification of the spin and orbital state in currents.
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