“Our findings are consistent with the second law of thermodynamics and emphasise the distinction between the concepts of irreversibility and time-reversal symmetry. Once the arrow of time and a particular low entropy initial condition at have been chosen, then the von Neumann entropy will increase forward in time from the temporal origin. However, a different choice of the arrow of time would have implied the same dynamics. The Markov approximation applied to the time-reversed evolution leads likewise to the same dissipation and entropy increase. Consequently any thermal equilibrium state for a forward-running trajectory is also an equilibrium thermal state for any time-reversed trajectory, and entropy increases in both directions: the system thermalises into both time directions. […]
“Furthermore, we speculate that these results may reflect on the cosmological arrow of time. In fact, the natural assumption that the universe was dissipative from time zero onwards would suggest that a model of it would rely on the Markov approximation performed at the moment of the Big Bang. If so, this would imply that two opposing arrows of time would have emerged from the Big Bang, which would account in turn for the maintenance of time-reversal symmetry despite the ensuing dissipative nature of the universe. We would happen to live in one of them, where dissipation and entropy increase are common experience, but unaware of the existence of the other alternative possibility.”
“Our findings are consistent with the second law of thermodynamics and emphasise the distinction between the concepts of irreversibility and time-reversal symmetry. Once the arrow of time and a particular low entropy initial condition at have been chosen, then the von Neumann entropy will increase forward in time from the temporal origin. However, a different choice of the arrow of time would have implied the same dynamics. The Markov approximation applied to the time-reversed evolution leads likewise to the same dissipation and entropy increase. Consequently any thermal equilibrium state for a forward-running trajectory is also an equilibrium thermal state for any time-reversed trajectory, and entropy increases in both directions: the system thermalises into both time directions. […]
“Furthermore, we speculate that these results may reflect on the cosmological arrow of time. In fact, the natural assumption that the universe was dissipative from time zero onwards would suggest that a model of it would rely on the Markov approximation performed at the moment of the Big Bang. If so, this would imply that two opposing arrows of time would have emerged from the Big Bang, which would account in turn for the maintenance of time-reversal symmetry despite the ensuing dissipative nature of the universe. We would happen to live in one of them, where dissipation and entropy increase are common experience, but unaware of the existence of the other alternative possibility.”