We analyze the dynamical evolution of a fluid with nonlinear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, algebraic, relaxation, and strong memory effects, presents scaling properties: the time evolution of the temperature-for both relaxation and memory effects-falls onto a master curve, regardless of the details of the experiment. To account for the observed behavior in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation-which considers not only the fourth cumulant but also the sixth one.
The overdamped Brownian dynamics of a harmonic oscillator is a paradigmatic system in non-equilibrium statistical mechanics, which reliably models relevant stochastic systems such as colloidal particles submitted to optical confinement. In this work, optimal thermal protocols are tailored to minimise the connection time between equilibrium states of overdamped d-dimensional oscillators. Application of control theory reveals that these optimal protocols are of bang-bang type, that is, the temperature of the bath has to take alternatively the minimum and maximum values allowed. Minimum connection times increase with the considered dimension d. Remarkably, this is the case even for symmetric oscillators, for example, with spherical symmetry—in which the degeneracy of the elastic constant along the d possible directions seems to imply a minimum connection time equal to that for the one-dimensional case. This surprising unavoidable price to pay when increasing dimension is thoroughly investigated and understood on a physical basis. Moreover, information theory tools such as the thermodynamic length and its divergence are analysed over the brachistochrone.
The overdamped Brownian dynamics of a harmonic oscillator is a paradigmatic system in non-equilibrium statistical mechanics, which reliably models relevant stochastic systems such as colloidal particles submitted to optical confinement. In this work, optimal thermal protocols are tailored to minimise the connection time between equilibrium states of overdamped d-dimensional oscillators. Application of control theory reveals that these optimal protocols are of bang-bang type, that is, the temperature of the bath has to take alternatively the minimum and maximum values allowed. Minimum connection times increase with the considered dimension d. Remarkably, this is the case even for symmetric oscillators, for example, with spherical symmetry-in which the degeneracy of the elastic constant along the d possible directions seems to imply a minimum connection time equal to that for the onedimensional case. This surprising unavoidable price to pay when increasing dimension is thoroughly investigated and understood on a physical basis. Moreover, information theory tools such as the thermodynamic length and its divergence are analysed over the brachistochrone.
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