QBS violates detailed balance at low temperatures.

[*Keldysh ordering and quantum polyspectra–* ]{} Consider first a classical noise process $\xi(t)$. Its moment generating function (MGF) is defined as $$\begin{aligned}
\label{Eq:MGFcl}
    \Lambda_{\rm class}[F(t); t_f] & = \overline{ \exp \left[ -i \int_0^{t_f} F(t) \xi(t) \right] },\end{aligned}$$ where the bar indicates a stochastic average. Functional derivatives of $\Lambda_{\rm class}$ with respect to $F(t)$ can be used to calculate arbitrary-order correlation functions of $\xi(t)$, while functional derivatives of $\ln \Lambda_{\rm class}$ generate the cumulants of $\xi(t)$ (see e.g. [@JacobsStochasticBook]). Fourier transforming these cumulants yields the polyspectra, which completely characterizes the noise in the frequency domain [@Rao1984book]. In the quantum case, our noise is a Heisenberg picture operator $\hat{\xi}(t)$ whose evolution is generated by the Hamiltonian of some bath; we take $\hat{\xi}(t)$ to be Hermitian for simplicity. Defining correlation functions now has some subtlety, as $\hat{\xi}(t)$ will not in general commute with itself at different times; hence, different time-ordering choices yield different results. Correlation functions at a given order describe both how the bath responds to external perturbations, as well as its intrinsic fluctuations [@Kamenev2011book]. We are interested here in characterizing the latter quantity, and asking whether these fluctuations are equivalent to an effective classical 