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Abstract
We study stochastic processes in which the trajectories are constrained so that the process realises a large deviation of the unconstrained process. In particular we consider stochastic bridges and the question of inequivalence of path ensembles between the microcanonical ensemble, in which the end points of the trajectory are constrained, and the canonical or s ensemble in which a bias or tilt is introduced into the process. We show how ensemble inequivalence can be manifested by the phenomenon of temporal condensation in which the large deviation is realised in a vanishing fraction of the duration (for long durations). For diffusion processes we find that condensation happens whenever the process is subject to a confining potential, such as for the Ornstein–Uhlenbeck process, but not in the borderline case of dry friction in which there is partial ensemble equivalence. We also discuss continuousspace, discretetime random walks for which in the case of a heavy tailed stepsize distribution it is known that the large deviation may be achieved in a single step of the walk. Finally we consider possible effects of several constraints on the process and in particular give an alternative explanation of the interactiondriven condensation in terms of constrained Brownian excursions.
Original language  English 

Article number  P12008 
Number of pages  23 
Journal  Journal of Statistical Mechanics: Theory and Experiment 
Volume  2015 
Issue number  12 
DOIs  
Publication status  Published  10 Dec 2015 
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 1 Finished

Design Principles for New Soft Materials
Cates, M., Allen, R., Clegg, P., Evans, M., MacPhee, C., Marenduzzo, D. & Poon, W.
7/12/11 → 6/06/17
Project: Research