Nonlinear Quantum Evolution Equations to Model Irreversible Adiabatic Relaxation with Maximal Entropy Production and Other Nonunitary Processes

Understand

We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors.

• The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator.
• It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics.
• We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems.