Generalized ensembles in the thermodynamics of trajectories

• Autores: Budini, Adrian Adolfo; Turner, Robert M.; Garrahan, Juan P.
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: LARGE DEVIATIONS IN NON-EQUILIBRIUM SYSTEMS; SLOW RELAXATION AND GLASSY DYNAMICS; STOCHASTIC PROCESSES (THEORY)
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This 'thermodynamics of trajectories' approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there are a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show how the LD functions that describe an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates can be mapped to those of the fixed-time ensemble. We discuss how the correspondence between generalized ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.
Fil: Budini, Adrian Adolfo. Universidad Tecnológica Nacional; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Turner, Robert M.. Science and Technology Facilities Council of Nottingham. Rutherford Appleton Laboratory; Reino Unido. University of Nottingham; Estados Unidos
Fil: Garrahan, Juan P.. Science and Technology Facilities Council of Nottingham. Rutherford Appleton Laboratory; Reino Unido. University of Nottingham; Estados Unidos