  The near-zero value of the cosmological constant \Lambda in an equilibrium
context may be due to the existence of a self-tuning relativistic vacuum
variable q. Here, a cosmological nonequilibrium context is considered with a
corresponding time-dependent cosmological parameter \Lambda(t) or vacuum energy
density \rho_V(t). A specific model of a closed Friedmann-Robertson-Walker
universe is presented, which is determined by equilibrium boundary conditions
at one instant of time (t=t_{eq}) and a particular form of vacuum-energy
dynamics (d\rho_V/dt \propto \rho_M). This homogeneous and isotropic model has
a standard Big Bang phase at early times (t << t_{eq}) and reproduces the main
characteristics of the present universe (t=t_0 < t_{eq}).
