hysteresisan

Hysteresisan is a theoretical construct in physics and materials science describing a class of memory-dependent response phenomena in which a system's present state reflects its past exposures beyond conventional hysteresis. Unlike standard hysteresis, where the response depends on current input history through a single loop, hysteresisan incorporates an auxiliary memory variable or nonlocal kernel that records a richer history of stimuli, leading to multi-loop or skewed response curves during cyclic forcing.

Models of hysteresisan typically employ an internal state variable h(t) coupled to the observable x(t). In a minimal representation, dx/dt = -∂U(x)/∂x + λ h, dh/dt = κ x − μ h, where U is a potential, and λ, κ, μ are parameters. Alternatively, h(t) can be defined as a time-nonlocal integral h(t) = ∫_0^t K(t−s) x(s) ds, with a fading memory kernel K. These formulations produce memory effects such as delayed responses, rounded loops, and multi-valued branches under cyclic inputs.

Occurrences of hysteresisan have been proposed to describe slow-relaxing polymer networks, certain ferroelectric or magnetic materials with complex defect landscapes, and climatic or ecosystem systems where past temperatures or fluxes influence current state beyond instantaneous forcing.

History and reception of the concept are mixed. The term was introduced in speculative literature in the mid-2010s and has since appeared in several theoretical works as a modeling concept, but it remains debated and not universally adopted. Critics argue it overlaps with established memory-effect frameworks and may be difficult to validate experimentally.

See also: hysteresis, memory effect, nonlocal dynamics, internal state variable models.