The orchestra plays in sync, but a hidden conductor changes the beat for a second. In the same way, a system moving toward equilibrium suddenly takes a step back.
Usually, if a system does not remember its past, it approaches equilibrium monotonically, like sand in an hourglass. But if it has memory, it can temporarily drift away from equilibrium. People had noticed this before, but they did not understand why it happens.
The author built simple models and found that if the memory is long, delayed feedback temporarily reverses the motion toward equilibrium. Then the usual proof of monotonicity stops working, and the distance to equilibrium can temporarily grow.
The orchestra is back in unison. Now it is clear that the stumble was not an accident but the work of memory, which briefly returned the system to its past.
In the Markovian case, relative entropy acts as a Lyapunov function that guarantees an irreversible approach to equilibrium. A loss of divisibility means the evolution cannot be split into successive Markovian steps, and then the familiar arrow of time can briefly turn backwards.