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We show that superconductors with broken time-reversal symmetry have veryspecific magnetic and electric responses to inhomogeneous heating. A localheating of such superconductors induces a magnetic field with a profile that issensitive to the presence of domain walls and crystalline anisotropy ofsuperconducting states. A nonstationary heating process produces an electricfield and a charge imbalance in different bands. These effects can be measuredand used to distinguish $s+is$ and $s+id$ superconducting states in thecandidate materials such as Ba$_{1-x}$K$_x$Fe$_2$As$_2$.

Thermoelectric Signatures of Time-Reversal Symmetry Breaking States in Multiband Superconductors