I had written before about the concept of Lazy States. Questions in non-equilibrium thermodynamics are usually said to be intractable, due to how much they depend on the details of the dynamical equations. We discovered that in quantum non-equilibrium thermodynamics, there was a simple way to separate the role of system-environment states and of the details of their Hamiltonian coupling. For a class of states, $$left[rho^{SE},rho^{S} right]=0$$ , Lazy States, the entropy rate is always zero independent of the interaction Hamiltonian. These Lazy States are rare, which opens the question of how come thermodynamic equilibrium is so common in the universe?
On a new paper in the arXiv titled Almost all states are pretty lazy, Adrian Hutter and Stephanie Wehner, from the Centre for Quantum Technologies in Singapore, tackled exactly this problem. They were able to show that even if states aren’t lazy, almost all states lead to dynamics which is very close to the ones generated by lazy states. Thus, even if systems are away from equilibrium, they cannot be too far away from it. This leads them to conclude that “Almost all states are pretty lazy”.
Minus Two Fish 