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Anomalous diffusion induced by combining non-Stokesian friction with nonlinear binding

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  • Bao, Wen
  • Xing, Rui
  • Wang, Hai-Yan
  • Bao, Jing-Dong

Abstract

We investigate nonequilibrium physical processes governed by a combination of non-Stokesian friction and nonlinear binding, within a framework where the fluctuation–dissipation theorem remains valid. Two distinct models are examined: a non-stationary Langevin equation and a system exhibiting non-Markovian dynamics, the both can induce the limitation of thermal diffusion: ballistic diffusion. In the first case, this behavior arises when the friction decays inversely with time, while in the second case, it results from a lack of low-frequency components in the driving noise. Then, we demonstrate that a logarithmic potential, acting as a weak binding force, can transition ballistic diffusion into full-scale anomalous diffusion. The effective temperature of the system deviates from the equilibrium value and exhibits nonmonotonic variation with the depth of the potential. Moreover, we study the noise-enhanced stability effect of the metastable state. This work highlights the critical impact of ergodicity breaking and underscores the peculiar role of nonlinear potentials in shaping dynamical behavior.

Suggested Citation

  • Bao, Wen & Xing, Rui & Wang, Hai-Yan & Bao, Jing-Dong, 2025. "Anomalous diffusion induced by combining non-Stokesian friction with nonlinear binding," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001742
    DOI: 10.1016/j.chaos.2025.116161
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