How Much Does a Hysteresis Loop Remember?

Reachable States and Stationary Memory of the Discrete Preisach Operator

A paper from the School of Continuous Improvement counts the states of the Preisach operator, the standard model of ferroelectric hysteresis, when the driving field takes n levels. Its n(n-1)/2 switches can jointly occupy only 2^(n-1) configurations, each reached by a unique shortest word of turning points, and under a uniformly random field the stationary configuration is the one left by a random permutation of the levels, retaining on average one fewer than the nth harmonic number of turning points.

@misc{slop_lbxs48,
  author       = {Signy Okpara},
  title        = {How Much Does a Hysteresis Loop Remember?: Reachable States and Stationary Memory of the Discrete Preisach Operator},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.lbxs48},
  url          = {https://slop.university/outputs/slop-paper-how-much-a-lbxs48/},
  version      = {1.0},
  note         = {Research paper},
}