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This book offers an informal, easy-to-understand account of topics
in modern physics and mathematics. The focus is, in particular, on
statistical mechanics, soft matter, probability, chaos, complexity,
and models, as well as their interplay. The book features 28 key
entries and it is carefully structured so as to allow readers to
pursue different paths that reflect their interests and priorities,
thereby avoiding an excessively systematic presentation that might
stifle interest. While the majority of the entries concern specific
topics and arguments, some relate to important protagonists of
science, highlighting and explaining their contributions. Advanced
mathematics is avoided, and formulas are introduced in only a few
cases. The book is a user-friendly tool that nevertheless avoids
scientific compromise. It is of interest to all who seek a better
grasp of the world that surrounds us and of the ideas that have
changed our perceptions.
This book offers an informal, easy-to-understand account of topics
in modern physics and mathematics. The focus is, in particular, on
statistical mechanics, soft matter, probability, chaos, complexity,
and models, as well as their interplay. The book features 28 key
entries and it is carefully structured so as to allow readers to
pursue different paths that reflect their interests and priorities,
thereby avoiding an excessively systematic presentation that might
stifle interest. While the majority of the entries concern specific
topics and arguments, some relate to important protagonists of
science, highlighting and explaining their contributions. Advanced
mathematics is avoided, and formulas are introduced in only a few
cases. The book is a user-friendly tool that nevertheless avoids
scientific compromise. It is of interest to all who seek a better
grasp of the world that surrounds us and of the ideas that have
changed our perceptions.
This brief offers a concise presentation of granular fluids from
the point of view of non-equilibrium statistical physics. The
emphasis is on fluctuations, which can be large in granular fluids
due to the small system size (the number of grains is many orders
of magnitude smaller than in molecular fluids). Firstly, readers
will be introduced to the most intriguing experiments on fluidized
granular fluids. Then granular fluid theory, which goes through
increasing levels of coarse-graining and emerging collective
phenomena, is described. Problems and questions are initially posed
at the level of kinetic theory, which describes particle densities
in full or reduced phase-space. Some answers become clear through
hydrodynamics, which describes the evolution of slowly evolving
fields. Granular fluctuating hydrodynamics, which builds a bridge
to the most recent results in non-equilibrium statistical
mechanics, is also introduced. Further and more interesting answers
come when the dynamics of a massive intruder are discussed. Such
non-equilibrium stochastic process offers a more precise and
compact picture of the features foreseen at the more detailed
levels of description. The dynamics of an intruder diffusing in a
granular fluid reveal the clearest connection with recent theories
on stochastic energetics and stochastic thermodynamics.
This book reviews the basic ideas of the Law of Large Numbers with
its consequences to the deterministic world and the issue of
ergodicity. Applications of Large Deviations and their outcomes to
Physics are surveyed. The book covers topics encompassing
ergodicity and its breaking and the modern applications of Large
deviations to equilibrium and non-equilibrium statistical physics,
disordered and chaotic systems, and turbulence.
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