  We propose a piecewise deterministic Markovian jump process in Hilbert space
such that the covariance matrix of this stochastic process solves the
thermodynamic quantum master equation. The proposed stochastic process is
particularly simple because the normalization of the vectors in Hilbert space
is preserved only on average. As a consequence of the nonlinearity of the
thermodynamic master equation, the construction of stochastic trajectories
involves the density matrix as a running ensemble average. We identify a
principle of detailed balance and a fluctuation-dissipation relation for our
Markovian jump process.
