For the arbitrary forces the extension-force dependence will be given by Langevin function:
2.
The spring force law is governed by inverse Langevin function or approximated by the Warner's relationship
3.
The Brillouin function is then simplified into the "'Langevin function "', named after Paul Langevin:
4.
In the case of isotropic magnetic materials, Boltzmann distribution can be reduced to Langevin function connecting isotropic anhysteretic magnetization with effective magnetic field H _ \ text { e }:
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