It is almost always implied that the fields of statistical physics/thermodynamics mostly consider systems in equilibrium. Simple things as defining the entropy become very hard once we are in the non-equilibrium regime.

Now I am studying quantum thermodynamics such as in this paper where I find it hard to distinguish between which processes keep the state in equilibrium and which processes don't.

To be more exact my questions are:

  1. How do I know a given set-up/process deals with the non-equilibrium regime?
  2. Assuming we have a harmonic oscillator initially in thermal state (which I assume to be in equilibrium), do unitaries that increase its energy keep it equilibrium or go into the non-equilibrium regime?

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