27,569 research outputs found
The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.Comment: 12 pages, submitted to Journal of Statistical Physic
The effective temperature
This review presents the effective temperature notion as defined from the
deviations from the equilibrium fluctuation-dissipation theorem in out of
equilibrium systems with slow dynamics. The thermodynamic meaning of this
quantity is discussed in detail. Analytic, numeric and experimental
measurements are surveyed. Open issues are mentioned.Comment: 58 page
Evolution of opinions on social networks in the presence of competing committed groups
Public opinion is often affected by the presence of committed groups of
individuals dedicated to competing points of view. Using a model of pairwise
social influence, we study how the presence of such groups within social
networks affects the outcome and the speed of evolution of the overall opinion
on the network. Earlier work indicated that a single committed group within a
dense social network can cause the entire network to quickly adopt the group's
opinion (in times scaling logarithmically with the network size), so long as
the committed group constitutes more than about 10% of the population (with the
findings being qualitatively similar for sparse networks as well). Here we
study the more general case of opinion evolution when two groups committed to
distinct, competing opinions and , and constituting fractions and
of the total population respectively, are present in the network. We show
for stylized social networks (including Erd\H{o}s-R\'enyi random graphs and
Barab\'asi-Albert scale-free networks) that the phase diagram of this system in
parameter space consists of two regions, one where two stable
steady-states coexist, and the remaining where only a single stable
steady-state exists. These two regions are separated by two fold-bifurcation
(spinodal) lines which meet tangentially and terminate at a cusp (critical
point). We provide further insights to the phase diagram and to the nature of
the underlying phase transitions by investigating the model on infinite
(mean-field limit), finite complete graphs and finite sparse networks. For the
latter case, we also derive the scaling exponent associated with the
exponential growth of switching times as a function of the distance from the
critical point.Comment: 23 pages: 15 pages + 7 figures (main text), 8 pages + 1 figure + 1
table (supplementary info
Mechanisms in Dynamically Complex Systems
In recent debates mechanisms are often discussed in the context of ‘complex systems’ which are understood as having a complicated compositional structure. I want to draw the attention to another, radically different kind of complex system, in fact one that many scientists regard as the only genuine kind of complex system. Instead of being compositionally complex these systems rather exhibit highly non-trivial dynamical patterns on the basis of structurally simple arrangements of large numbers of non-linearly interacting constituents. The characteristic dynamical patterns in what I call “dynamically complex systems” arise from the interaction of the system’s parts largely irrespective of many properties of these parts. Dynamically complex systems can exhibit surprising statistical characteristics, the robustness of which calls for an explanation in terms of underlying generating mechanisms. However, I want to argue, dynamically complex systems are not sufficiently covered by the available conceptions of mechanisms. I will explore how the notion of a mechanism has to be modified to accommodate this case. Moreover, I will show under which conditions the widespread, if not inflationary talk about mechanisms in (dynamically) complex systems stretches the notion of mechanisms beyond its reasonable limits and is no longer legitimate
Joint effect of ageing and multilayer structure prevents ordering in the voter model
The voter model rules are simple, with agents copying the state of a random
neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the
model has also applications for catalysis and species competition. Inspired by
the temporal inhomogeneities found in human interactions, one can introduce
ageing in the agents: the probability to update decreases with the time elapsed
since the last change. This modified dynamics induces an approach to consensus
via coarsening in complex networks. Additionally, multilayer networks produce
profound changes in the dynamics of models. In this work, we investigate how a
multilayer structure affects the dynamics of an ageing voter model. The system
is studied as a function of the fraction of nodes sharing states across layers
(multiplexity parameter q ). We find that the dynamics of the system suffers a
notable change at an intermediate value q*. Above it, the voter model always
orders to an absorbing configuration. While, below, a fraction of the
realizations falls into dynamical traps associated to a spontaneous symmetry
breaking in which the majority opinion in the different layers takes opposite
signs and that due to the ageing indefinitely delay the arrival at the
absorbing state.Comment: 10 pages, 8 figure
- …