83 research outputs found
The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments
Full text linkThere has been great interest in applying the results of statistical
mechanics to single molecule experiements. Recent work has highlighted
so-called non-equilibrium work-energy relations and Fluctuation Theorems which
take on an equilibrium-like (time independent) form. Here I give a very simple
heuristic example where an equilibrium result (the barometric law for colloidal
particles) arises from theory describing the {\em thermodynamically}
non-equilibrium phenomenon of a single colloidal particle falling through
solution due to gravity. This simple result arises from the fact that the
particle, even while falling, is in {\em mechanical} equilibrium (gravitational
force equal the viscous drag force) at every instant. The results are
generalized by appeal to the central limit theorem. The resulting time
independent equations that hold for thermodynamically non-equilibrium (and even
non-stationary) processes offer great possibilities for rapid determination of
thermodynamic parameters from single molecule experiments.Comment: 6 page
Self-similar disk packings as model spatial scale-free networks
Full text linkThe network of contacts in space-filling disk packings, such as the
Apollonian packing, are examined. These networks provide an interesting example
of spatial scale-free networks, where the topology reflects the broad
distribution of disk areas. A wide variety of topological and spatial
properties of these systems are characterized. Their potential as models for
networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of
higher-dimensional packing
Colloquium: Statistical mechanics of money, wealth, and income
Full text linkThis Colloquium reviews statistical models for money, wealth, and income
distributions developed in the econophysics literature since the late 1990s. By
analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown
that the probability distribution of money is exponential for certain classes
of models with interacting economic agents. Alternative scenarios are also
reviewed. Data analysis of the empirical distributions of wealth and income
reveals a two-class distribution. The majority of the population belongs to the
lower class, characterized by the exponential ("thermal") distribution, whereas
a small fraction of the population in the upper class is characterized by the
power-law ("superthermal") distribution. The lower part is very stable,
stationary in time, whereas the upper part is highly dynamical and out of
equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of
references corresponding to the published versio
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