**Exploring universality classes of
nonequilibrium statistical physics**

Universal scaling behavior is an attractive feature
in statistical physics because a wide range of models can be
classified purely in terms of their collective behavior due to a
diverging correlation length. Scaling phenomenon has been observed
in many branches of physics, chemistry, biology, economy ... etc.,
most frequently by **critical
phase transitions and surface growth.**
This is a basic science topic, the results can be used
in applied sciences:

Nonequilibrium
**critical
phase transitions**
appear
in models of*Spatiotemporal
intermittency** :
*Z.
Jabeen and N. Gupte, Phys. Rev. E 72 (2005) 016202,

The concept of self-organized critical (SOC) phenomena has been introduced some time ago to explain the frequent occurrences of

Rough

Understanding the fundamental laws driving the tumor development is one of the biggest challenges of contemporary science. Internal

In application to

Earlier most of the models were investigated on regular

In
the past few years the interest is focused on the research of
**complex
networks**
(R.
Albert and A.-L. Barabasi, Rev. Mod. Phys. **74**,
47 (2002).
Recently the dynamics and the phase transitions of network systems
is under study (M. Aldana
and H. Larralde, Phys. Rev. E **70**,
066130 (2004)). Contrary
to the regular lattices universality in network models is not so
well defined, scaling (if exists) depends on the underlying topology [57],[59],[62],[64],[73 ].

Nonequilibrium
systems can be classified into two categories:

(a) Systems which
do have a hermitian Hamiltonian and whose stationary states are
given by the proper Gibbs-Boltzmann distribution. However, they are
prepared in an initial condition which is far from the stationary
state and sometimes, in the thermodynamic limit, the system may
never reach the true equilibrium. These nonequilibrium systems
include, for example, phase ordering systems, spin glasses, glasses
etc... and are defined by adding simple dynamics to static
models.

(b) Systems without a hermitian Hamiltonian defined by
transition rates, which do not satisfy the detailed balance
condition (the local time reversal symmetry is broken). They may or
may not have a steady state and even if they have one, it is not a
Gibbs state. Such models can be created by combining different
dynamics or by generating currents in them externally. The critical
phenomena of these systems are referred here as ``Out of equilibrium
classes''. There are also systems, which are not related to
equilibrium models, in the simplest case these are lattice Markov
processes of interacting particle systems (T. Ligget, Interacting
particle systems (Springer-Verlag, Berlin, 1985)). These are
referred here as ``Genuinely non-equilibrium systems''.

For more
details see: Géza Ódor: *Universality
classes in nonequilibrium lattice systems*
Rev.
Mod. Phys. 76 (2004) 663.

or the book published in
2008 by World Scientific:
http://www.worldscibooks.com/physics/6813.html

*Aug 29, 2012*