Microscopic bath effects on noise spectra in semiconductor quantum dot qubits

When a system is thermally coupled to only small part of larger bath, statistical fluctuations the temperature (more precisely, internal energy) this ``sub-bath'' around mean defined by bath can become significant. We show that these generally give rise $1/f$-like noise power spectral density from even single two-level system. extend results distribution fluctuators, finding corresponding modification Dutta-Horn relation. Then we consider specific situation charge in silicon quantum dot qubits and recent experimental data [E. J. Connors et al., Phys. Rev. B 100, 165305 (2019)] be modeled as arising few two accounting for sub-bath size improves quality fit.