Well here is their conclusion
"In this paper, we have outlined a general systems theory framework for thermodynamics. The proposed macroscopic
mathematical model is based on a nonlinear compartmental system model that is characterized by energy
conservation laws capturing the exchange of energy between coupled macroscopic subsystems. This dynamical system
formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a
mathematically rigorous formulation for thermodynamical systems out of equilibrium. While it seems impossible to
reduce thermodynamics to a mechanistic world picture due to microscopic reversibility and Poincaré recurrence, our
system thermodynamic formulation provides a harmonization of classical thermodynamics with classical mechanics
by developing clear connections between system irreversibility, absence of Poincaré recurrence, the second law of
thermodynamics, and the entropic arrow of time."
The entropy is indeed parallal if you prefer with time.If we take all our dynamics, time is constant .And the entropy increases on this timeline.It's pure thermodynamics, Boltzmann will agree.
If you think that at the Planck Scale you shall check Time.It's time to return at reason.
If you think that our psychology is different than our physicality, I suspect a problem of objectivity.The universe is more than a computer.
If you see well the timeline, you shall see the increase of entropy due to evolution, but never this timeline can be extrapolated in this no sense(its reversibility).
The Determinism for time is essential.
In Biology ,the irreversibility is evident.
If as Prigogine said, for physics time can be reversible, don't misinterpret his words,....you must differenciate your philosophical perception and our reality and the allow of time.
Steve