Under certain conditions, two samples of fluid at different initial temperatures present a counterintuitive behavior known as the Mpemba effect: it is the hotter system that cools sooner. Here, we show that the Mpemba effect is present in granular fluids, both in uniformly heated and in freely cooling systems. In both cases, the system remains homogeneous, and no phase transition is present. Analytical quantitative predictions are given for how differently the system must be initially prepared to observe the Mpemba effect, the theoretical predictions being confirmed by both molecular dynamics and Monte Carlo simulations. Possible implications of our analysis for other systems are also discussed.

Ergodicity breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical and quantum settings. These phenomena are typically associated with phase transitions, e.g., the emergence of metastable regimes near a first-order transition or scaling dynamics in the vicinity of critical points. Despite being of fundamental interest the associated divergent timescales are a hindrance when trying to explore steady-state properties. Here we show that the relaxation dynamics of Markovian open quantum systems can be accelerated exponentially by devising an optimal unitary transformation that is applied to the quantum system immediately before the actual dynamics. This initial “rotation” is engineered in such a way that the state of the quantum system no longer excites the slowest decaying dynamical mode. We illustrate our idea—which is inspired by the so-called Mpemba effect, i.e., water freezing faster when initially heated up—by showing how to achieve an exponential speeding-up in the convergence to stationarity in Dicke models, and how to avoid metastable regimes in an all-to-all interacting spin system.

According to conventional wisdom, a system placed in an environment with a different temperature tends to relax to the temperature of the latter, mediated by the flows of heat or matter that are set solely by the temperature difference. It is becoming clear, however, that thermal relaxation is much more intricate when temperature changes push the system far from thermodynamic equilibrium. Here, by using an optically trapped colloidal particle, we show that microscale systems under such conditions heat up faster than they cool down. We find that between any pair of temperatures, heating is not only faster than cooling but the respective processes, in fact, evolve along fundamentally distinct pathways, which we explain with a new theoretical framework that we call thermal kinematics. Our results change the view of thermalization at the microscale and will have a strong impact on energy-conversion applications and thermal management of microscopic devices, particularly in the operation of Brownian heat engines.

We analyze the fluctuations of the dissipated energy in a simple and general model where dissipation, diffusion, and driving are the key ingredients. The full dissipation distribution, which follows from hydrodynamic fluctuation theory, shows non-Gaussian tails and no negative branch, thus violating the fluctuation theorem as expected from the irreversibility of the dynamics. It exhibits simple scaling forms in the weak- and strong-dissipation limits, with large fluctuations favored in the former case but strongly suppressed in the latter. The typical path associated with a given dissipation fluctuation is also analyzed in detail. Our results, confirmed in extensive simulations, strongly support the validity of hydrodynamic fluctuation theory to describe fluctuating behavior in driven dissipative media.

We consider the problem of how a condensed molecular system approaches equilibrium, focusing on the particular case of water. We show, by means of extensive molecular dynamics simulations, that the existence of different types of degrees of freedom affects the dynamics of equilibration, and this influence is made most obvious in the system's temperature. When equipartition of energy does not hold in the initial, nonequilibrium state, the instantaneous temperature can be up to a few degrees lower than that observed under equipartition conditions, resulting in a Mpemba-like effect. Though our study considers water in particular, our findings apply more generally to condensed molecular systems.

We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated with a path in mesoscopic phase space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in nondissipative systems. This is a consequence of the quasielasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always Gaussian, as expected from the central limit theorem. On the other hand, strong separation from the Gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem, as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily suppressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion, and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases nonconvex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of describing in detail the fluctuating behavior of nonlinear driven dissipative media. DOI: http://dx.doi.org/10.1103/PhysRevE.88.022110 ©2013 American Physical Society