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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Spin Networks

Background:

  • Progressive quenching (PQ) sequentially fixes system degrees of freedom.
  • PQ processes may not satisfy local detailed balance.
  • Certain observables in spin networks exhibit martingale properties.

Purpose of the Study:

  • Investigate system response to perturbations during PQ.
  • Analyze the origin of persistent memory in PQ.
  • Explore the predictive power of the martingale property.

Main Methods:

  • Perturbation analysis at intermediate PQ stages.
  • Examination of system observables and probability distributions.
  • Application of hidden martingale process theory.

Main Results:

  • Final stage response reveals persistent memory.
  • Persistence is directly linked to the underlying martingale process.
  • The shape of the probability distribution is also memorized.
  • Predicts final bimodal distribution from early unimodal states.

Conclusions:

  • Martingale property acts as a stochastic conservation law in PQ.
  • Martingale property explains persistent memory and distribution shape retention.
  • Proposes stochastic invariance as supporting evidence for this conservation law.