Abstract:
Statisticalmechanics is an essential tool to describe the behavior of complex systems ranging
frombacterial growth to universe expansion. For a systemin equilibrium, this approach
is well established and the stationary state distribution is given by the Boltzmann weight.
Nonequilibrium systems are much more common than the equilibrium ones but a complete
formalism analogous to equilibrium statistical mechanics has not been developed
for nonequilibrium processes. We therefore study some simple nonequilibrium models
in detail to gain an insight in these systems. In this thesis, we focus on one-dimensional
nonequilibrium interacting particle systems which are driven by an external force. Such
systems can show a non-trivial phase transition even in one-dimension and we are interested
in understanding the critical behavior of these systems. The models studied in this
thesis aremotivated by the common phenomenon of jamming that occurs in traffic flow of
vehicles,molecularmotors, fluid flow through narrow pipe, etc.
In this thesis, we study two generic classes of one-dimensional stochastic models: (a)
lattice gasmodels of hard core particles in which a particle hops to an empty site according
to the hop rule assigned to it and (b)mass transportmodels in which each site can contain
many particles and a particle hops to another site according to the prescribed rule. Below
we list four lattice gas models that we have worked on in this thesis and their correspondence
to themass transportmodels:
