Entropy distribution of a two-level system: An asymptotic analysis

Simple solvable energy-landscape model that shows a thermodynamic phase transition and a glass transition

When a liquid melt is cooled, a glass or phase transition can be obtained depending on the cooling rate. Yet, this behavior has not been clearly captured in energy-landscape models. Here, a model is provided in which two key ingredients are considered in the landscape, metastable states and their multiplicity. Metastable states are considered as in two level system models. However, their multiplicity and topology allows a phase transition in the thermodynamic limit for slow cooling, while a transition to the glass is obtained for fast cooling. By solving the corresponding master equation, the minimal speed of cooling required to produce the glass is obtained as a function of the distribution of metastable states.

Probability distribution of work done on a two-level system during a nonequilibrium isothermal process

We present an exact calculation of the probability density for the work done by an external agent on a two-level system. Due to the external drive, both the transition rates between the two states and their energies depend on time. Within this setting we calculate the probability of every possible sample path of the system evolution and also the work done along any such path. The general procedure yields an evolution equation for the characteristic function of the work. Assuming that the energies change with constant rates, the properties of the work distribution are controlled by a single parameter representing the ratio of the time scales of the driving protocol, and of the internal dynamics, respectively. We calculate the mean work and characterize those sample paths which are not in agreement with the second law. In the slow driving limit, the probability density for the work collapses to a delta function localized at the reversible work. In the strongly nonequilibrium regime, the most probable work is smaller and the mean work is bigger than the reversible work.

Glasslike dynamical behavior in hierarchical models submitted to continuous cooling and heating processes

The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature processes. In cooling processes, a phenomenon analogous to the laboratory glass transition appears. The residual properties are analytically evaluated, and the concept of fictive temperature is discussed on a physical basis. The evolution of the system in heating processes is governed by the existence of a normal solution of the evolution equations, which is approached by all the other solutions. This trend of the system is directly related to the glassy hysteresis effects shown by these systems. The existence of the normal solution is not restricted to the linear regime around equilibrium, but it is defined for any arbitrary, far-from-equilibrium, situation.