Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

arXiv:2204.08260EntropyJan 9, 20234 citations

Steepest-entropy-ascent nonequilibrium quantum thermodynamic framework to model chemical reaction rates at an atomistic level

Gian Paolo Beretta, Omar Al-Abbasi, Michael R. von Spakovsky

The steepest entropy ascent (SEA) dynamical principle provides a general framework for modeling the dynamics of nonequilibrium (NE) phenomena at any level of description, including the atomistic one. It has recently been shown to provide a precise implementation and meaning to the maximum entropy production principle and to encompass many well-established theories of nonequilibrium thermodynamics into a single unifying geometrical framework. Its original formulation in the framework of quantum thermodynamics (QT) assumes the simplest and most natural Fisher-Rao metric to geometrize from a dynamical standpoint the manifold of density operators, which represent the thermodynamic NE states of the system. This simplest SEAQT formulation is used here to develop a general mathematical framework for modeling the NE time evolution of the quantum state of a chemically reactive mixture at an atomistic level. The method is illustrated for a simple two-reaction kinetic scheme of the overall reaction F+H_{2}⇔HF+F in an isolated tank of fixed volume. However, the general formalism is developed for a reactive system subject to multiple reaction mechanisms. To explicitly implement the SEAQT nonlinear law of evolution for the density operator, both the energy and the particle number eigenvalue problems are set up and solved analytically under the dilute gas approximation. The system-level energy and particle number eigenvalues and eigenstates are used in the SEAQT equation of motion to determine the time evolution of the density operator, thus effectively describing the overall kinetics of the reacting system as it relaxes toward stable chemical equilibrium. The predicted time evolution in the near-equilibrium limit is compared to the reaction rates given by a standard detailed kinetic model so as to extract the single time constant needed by the present SEA model.

arXiv:1504.03994Physical review. EApr 24, 201721 citations