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Steepest entropy ascent solution for a continuous-time quantum walker.

Rohit Kishan Ray1

  • 1Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India.

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The steepest entropy ascent (SEA) principle, a potential fourth law of thermodynamics, drives quantum systems toward equilibrium. This study introduces a new method to approximate SEA evolution for quantum walkers, revealing dissipation dynamics and qubit trajectories.

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Area of Science:

  • Quantum Thermodynamics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • The steepest entropy ascent (SEA) principle describes the nonlinear thermodynamic evolution of quantum systems, potentially representing a fourth law of thermodynamics.
  • SEA posits a unique global equilibrium state towards which all other states evolve via maximum entropy generation.

Purpose of the Study:

  • To investigate the SEA evolution of a continuous-time quantum walker (CTQW) on a cycle graph.
  • To develop an approximate analytical scheme for SEA solutions, which are typically difficult to obtain.
  • To analyze the resulting dissipation dynamics and quantum trajectories.

Main Methods:

  • Introduction of the fixed Lagrange's multiplier (FLM) method for approximating SEA evolution.
  • Application of the FLM method to a single-particle evolution equation for CTQW.
  • Analysis of Bloch vector trajectories in the Bloch sphere representation for a qubit.
  • Characterization of decoherence in CTQW using probability amplitudes.

Main Results:

  • The FLM scheme successfully generates dissipation dynamics for quantum systems under SEA.
  • Distinct trajectories of the Bloch vector were observed within the Bloch sphere for a qubit.
  • Similar dissipative motion and decoherence were observed in CTQW, with strong delocalization at low system relaxation times.
  • The FLM scheme demonstrated good agreement with numerical simulations.

Conclusions:

  • The FLM method provides a viable approach for studying SEA in complex quantum systems like CTQW.
  • SEA dynamics lead to observable dissipation and decoherence, influencing quantum system evolution.
  • Understanding these dynamics is crucial for controlling quantum states and mitigating decoherence.