Speaker
David Saad
(Aston University Birmingham)
Description
Equilibrium is a fundamental concept in statistical physics; it
assumes that while the system dynamics is governed by
microscopic interactions, some systems eventually reach a
state where macroscopic observables remain unchanged. The
evolution of many such systems is driven by the
corresponding Hamiltonian energy function and their states
converge to the equilibrium Gibbs-Boltzmann distribution,
from which all macroscopic properties can be computed.
However, the process governing the dynamics of many other
systems cannot be derived from a Hamiltonian; such systems
neither obey detailed balance nor converge to an equilibrium
state. While many real systems, for example in the financial,
social and biological areas, are inherently not in equilibrium,
some of their constituents exhibit equilibrium-like behaviour
in emerging localised or non-localised domains. In this work
we show such behaviour in model systems defined on densely
and sparsely connected networks, as they provide a useful
representation of many natural and technological systems.
Equilibrium domains are shown to emerge either abruptly or
gradually depending on the system parameters, for instance
temperature, and disappear, becoming indistinguishable from
the remainder of the system for other parameter values.
Consequently, such domains may exist, under some
conditions, within a non-equilibrium system but may be
difficult to identify.
