Thermodynamically consistent Langevin dynamics with spatially correlated noise predicting frictionless regime and transient attraction effect

Bounding energy growth in frictionless stochastic oscillators

This paper presents analytical and numerical results on the energetics of nonharmonic, undamped, single-well, stochastic oscillators driven by additive Gaussian white noises. The absence of damping and the action of noise are responsible for the lack of stationary states in such systems. We explore the properties of average kinetic, potential, and total energies along with the generalized equipartition relations. It is demonstrated that in frictionless dynamics, nonequilibrium stationary states can be produced by stochastic resetting. For an appropriate resetting protocol, the average energies become bounded. If the resetting protocol is not characterized by a finite variance of renewal intervals, stochastic resetting can only slow down the growth of the average energies but it does not bound them. Under special conditions regarding the frequency of resets, the ratios of the average energies follow the generalized equipartition relations.

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.