Steepest Entropy Ascent model for far-non-equilibrium dissipative evolution in quantum thermodynamics: a 1984 precursor of GENERIC (1997), gradient flows (1998), maximal entropy production (2001), and SEAQT (2014)
Gian Paolo Beretta (Università di Brescia (Italy))
Mon, 05 Mar 2018 • 11:00-11:40h • Templergraben 55, Lecture Hall V
- We have shown in  that the dissipative (irreversible) structure of several mathematical frameworks for modeling nonequilibrium states and their dynamics can be unified by extending the idea of steepest entropy ascent (SEA) that we first introduced in  in quantum thermodynamics (QT) modeling. Such frameworks include: Small-Scale and Rarefied Gases Dynamics (Boltzmann equation and its kinetic models); Rational Extended Thermodynamics, Macroscopic Non-Equilibrium Thermodynamics, and Chemical Kinetics; Mesoscopic Non-Equilibrium Thermodynamics; Quantum Computing . In  we proved that the dissipative part of the nonequilibrium formulation known as GENERIC is essentially an implementation of the SEA principle: whenever the GENERIC structure is equipped with an inner product, the SEA and GENERIC models of the irreversible component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. The talk will show as case study the use of SEA to develop models of the Boltzmann equation .
In  SEAQT has been used to model effectively quantum decoherence. By combining the SEA principle in the QT framework with a constrained-equilibrium (or hypoequilibrium) model reduction approach, Ref.  developed the SEAQT approach into a quantum statistical thermodynamic analysis of nonequilibrium evolution, especially effective in providing far-from-equilibrium time-dependent information also for macroscopic and mesoscopic systems. Rather than from a phenomenological description, the method starts from a more fundamental density-of-states representation of existing models of the system’s eigenstructure (see e.g. ).
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