Steepest entropy ascent in Quantum Thermodynamics

Gershon Kurizki, Nilakantha Meher, Avijit Misra +2 more

Ilki Kim, Michael R. von Spakovsky

Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intrarelaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time is valid as well for time-independent Hamiltonians as a special case and makes the description provided by the SEAQT framework more robust at the fundamental level. In addition, the SEAQT framework is used to help resolve a fundamental issue of thermodynamics in the quantum domain, namely, that concerning the unique definition of process-dependent work and heat functions. The developments presented lead to the conclusion that this framework is not just an alternative approach to thermodynamics in the quantum domain but instead one that uniquely sheds new light on various fundamental but as of yet not completely resolved questions of thermodynamics.

H.L. Varela, Angelo Plastino

Robert Tyler Holladay

Quantum information and quantum computing (QIQC) systems, relying on the phenomena of superposition and entanglement, offer the potential for vast improvements in certain computations. A practical QC realization requires maintaining the stored information for time-scales long enough to implement algorithms. One primary cause of information loss is decoherence, i.e., the loss of coherence between two energy levels in a quantum system. This work attributes decoherence to dissipation occurring as the system evolves and uses steepest-entropy-ascent quantum thermodynamics (SEAQT) to predict the evolution of system state. SEAQT asserts that, at any instant of time, the system state evolves such that the rate of system entropy change is maximized while conserving system energy. With this principle, the SEAQT equation of motion is applicable to systems in any state, near or far from stable equilibrium, making SEAQT particularly well suited for predicting the dissipation occurring as quantum algorithms are implemented. In the present research, the dynamics of qubits (quantum-bits) using the SEAQT framework are first examined during common quantum gates (combinations of which form algorithms). This is then extended to modeling a system of multiple qubits implementing Shor's algorithm on a nuclear-magnetic-resonance (NMR) QC. Additionally, the SEAQT framework is used to predict experimentally observed dissipation occurring in a two-qubit NMR QC undergoing a so called ``quenching'' process. In addition, several methods for perturbing the density or so-called ``state'' operator used by the SEAQT equation of motion subject to an arbitrary set of expectation value constraints are presented. These are then used as the basis for randomly generating states used in analyzing the dynamics of entangled, non-interacting systems within SEAQT. Finally, a reservoir interaction model is developed for general quantum systems where each system locally experiences a heat interaction with an external reservoir. This model is then used as the basis for developing a decoherence control scheme, which effectively transfers entropy out of the QIQC system as it is generated, thus, reducing the decoherence. Reservoir interactions are modeled for single qubits and the control scheme is employed in modeling an NMR QC and shown to eliminate nearly all of the noise caused by decoherence/dissipation.

Göran Lindblad

César Damián, Robert Tyler Holladay, Michael R. von Spakovsky +1 more

Abstract This work presents an analysis of the evolution of perturbed Bell diagonal states using the equation of motion of steepest-entropy-ascent quantum thermodynamics (SEAQT), the Lindblad equation, and various measures of entanglement loss. The Bell diagonal states considered are those generated by the quantum optics study conducted by Liu et al (2016 Phys. Rev. A 94 062107). First, a brief derivation is provided, showing that Bell diagonal states are stationary but not stable equilibrium states within the SEAQT formalism. This highlights the need for perturbation methods to study the evolution of nearby states with, for example, similar values of the energy and entropy. In contrast, under the Lindblad equation of motion, only some Bell diagonal states remain stationary. Although SEAQT is a non-standard, nonlinear framework, it exhibits several unique features that other approaches do not. In particular, not only does it satisfy the postulates of quantum mechanics, but it, as well, is fully compatible with the second law of thermodynamics, providing a physically consistent description of non-equilibrium quantum systems. The perturbation methods used include a weighted-average method for perturbing bipartite system states and a general bipartite method based on a set of unitary operations constrained to maintain constant system energy and entropy. Sets of density operators are randomly generated using each method, and the resulting time-dependent characteristics of the entanglement are analyzed within the SEAQT and Lindblad frameworks. The findings reveal that the evolutions associated with constrained perturbations accurately predict the loss of non-locality and align well with measured concurrence. Additionally, within the SEAQT framework, the deep connection between the thermodynamic states of the evolution of the system and the loss of non-locality is quantitatively demonstrated.