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

Mesoscale and Nanoscale Physics;Quantum Physics