Steepest Entropy Ascent Solution for a Continuous-Time Quantum Walker
arXiv:1907.04548 · doi:10.1103/PhysRevE.106.024115
Abstract
We consider the steepest entropy ascent (SEA) ansatz to describe the non-linear thermodynamic evolution of a quantum system. Recently this principle has been dubbed the fourth law of thermodynamics (Beretta Gian Paolo. 2020 The fourth law of thermodynamics: steepest entropy ascent). A unique global equilibrium state exists in this context, and any other state is driven by the maximum entropy generation principle towards this equilibrium. We study the SEA evolution of a continuous-time quantum walker (CTQW) on a cycle graph with N nodes. SEA solutions are difficult to find analytically. We provide an approximate scheme to find a general single-particle evolution equation governed by the SEA principle, whose solution produces dissipation dynamics. We call this scheme fixed Lagrange's multiplier (FLM) method. In the Bloch sphere representation, we find trajectories traced out by the Bloch vector within the sphere itself. We have discussed these trajectories under various initial conditions for the case of a qubit. A similar dissipative motion is also observed in the case of CTQW, where probability amplitudes have been used to characterize decoherence. Our FLM scheme shows good agreement with numerical results. As reported in the text, in CTQW, a strong delocalization exists for low system relaxation time.
18 pages,11 figures
References in corpus (17)
- Universal computation by quantum walk
- Spatial search by quantum walk
- Bloch vectors for qudits
- Decoherence in quantum walks - a review
- Connecting the discrete and continuous-time quantum walks
- Quantum Walk on a Line with Two Entangled Particles
- Quantum random walk of two photons in separable and entangled state
- Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle
- The fourth law of thermodynamics: steepest entropy ascent
- Essential equivalence of the GENERIC and Steepest Entropy Ascent models of dissipation for non-equilibrium thermodynamics
- How fast do quantum walks mix?
- Thermodynamic formalism for dissipative quantum walks
- Nonequilibrium thermodynamics: emergent and fundamental
- Thermodynamics of N-dimensional quantum walks
- Continuous-Time Quantum Random Walks Require Discrete Space
- Continuous-time quantum walks in the presence of a quadratic perturbation
- Qubit thermodynamics far from equilibrium: two perspectives about the nature of heat and work in the quantum regime