Metastability for Markov processes with detailed balance

We present a definition for metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance. In particular, we identify a crucial condition that distinguishes metastable states from other slow decaying modes and which allows us to show that our definition has several desirable properties similar to those postulated in the restricted ensemble approach. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible.     

Fluctuation-dissipation theorem for metastable systems

We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.     

Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.     

Violation of the zeroth law of thermodynamics in systems with negative specific heat

We show that systems with negative specific heat can violate the zeroth law of thermodynamics. By both numerical simulations and by using exact expressions for free energy and microcanonical entropy, it is shown that if two systems with the same intensive parameters but with negative specific heat are thermally coupled, they undergo a process in which the total entropy increases irreversibly. The final equilibrium is such that two phases appear; that is, the subsystems have different magnetizations and internal energies at temperatures which are equal in both systems, but that can be different from the initial temperature.     

Kinetics of shape equilibration for two dimensional islands

We study the relaxation to equilibrium of two dimensional islands containing up to 20 000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets: this allows us to explain both the activation energy and the island size dependence of the equilibration time. Received 7 December 1998 and Received in final form 18 March 1999     

Transport Properties of a Modified Lorentz Gas

We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed freely-rotating circular scatterers interacting with point particles via perfectly rough collisions. Upon imposing a temperature and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds for low values of the imposed gradients. Transport in this system is normal, in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are non-trivially coupled, satisfying Onsager's reciprocity relations to within numerical accuracy as well as the Green–Kubo relations. We further show numerically that an applied electric field causes the same currents as the corresponding chemical potential gradient in first order of the applied field. Puzzling discrepancies in higher order effects (Joule heating) are also observed. Finally, the role of entropy production in this purely Hamiltonian system is shortly discussed.     

A definition of metastability for Markov processes with detailed balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach [1]. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.