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It is known that in the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory function), the generalized Langevin equation may have non-ergodic solutions which do not relax to equilibrium values. It is shown that the equation may have non-ergodic (non-stationary) solutions even if the integral of the memory function is finite and diffusion is normal.
Approximate analytical solutions of the modified Langevin equation are obtained. These solutions are relatively simple and enough accurate. They are illustrated by considering a mean-field model of a system with interacting superparamagnetic particle
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject
The ultimate goal of physics is finding a unique equation capable of describing the evolution of any observable quantity in a self-consistent way. Within the field of statistical physics, such an equation is known as the generalized Langevin equation
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an effective thermal equilibrium even though