Fig. 2
From: Emergence of opposing arrows of time in open quantum systems
The von Neunmann entropy \(S_{\textsc {vN}}\) of the solution44 to the time-symmetric quantum Brownian motion master equation (42), in a pure state at \(t=0\). Here \(\gamma =M=k_{B}T = \hbar = 1\). The von Neumann entropy is calculated from the purity45, and increases unbounded as the off-diagonal terms of the density operator in the momentum representation decay to zero. The entropy increases (irreversibility) in both temporal directions but there is nonetheless no arrow-of-time, as time-reversal symmetry is maintained. Increasing entropy only indicates motion away from the temporal origin, not whether system is moving forwards or backwards in time.
