  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 is 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 that an ensemble of trajectories where
some time-extensive quantity is constant (and large) but where total
observation time fluctuates, is equivalent to the fixed-time ensemble, and the
LD functions that describe one ensemble can be obtained from those that
describe the other. We discuss how the equivalence between generalised
ensembles can be exploited in path sampling schemes for generating rare
dynamical trajectories.
