103,470 research outputs found
Differential entropy and time
We give a detailed analysis of the Gibbs-type entropy notion and its
dynamical behavior in case of time-dependent continuous probability
distributions of varied origins: related to classical and quantum systems. The
purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon)
entropies is explained in case of non-equilibrium Smoluchowski processes. A
very different temporal behavior of Gibbs and Kullback entropies is confronted.
A specific conceptual niche is addressed, where quantum von Neumann, classical
Kullback-Leibler and Gibbs entropies can be consistently introduced as
information measures for the same physical system. If the dynamics of
probability densities is driven by the Schr\"{o}dinger picture wave-packet
evolution, Gibbs-type and related Fisher information functionals appear to
quantify nontrivial power transfer processes in the mean. This observation is
found to extend to classical dissipative processes and supports the view that
the Shannon entropy dynamics provides an insight into physically relevant
non-equilibrium phenomena, which are inaccessible in terms of the
Kullback-Leibler entropy and typically ignored in the literature.Comment: Final, unabridged version; http://www.mdpi.org/entropy/ Dedicated to
Professor Rafael Sorkin on his 60th birthda
Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions
Macroscopic thermodynamics of equilibrium is constructed for systems obeying
power-law canonical distributions. With this, the connection between
macroscopic thermodynamics and microscopic statistical thermodynamics is
generalized. This is complementary to the Gibbs theorem for the celebrated
exponential canonical distributions of systems in contact with a heat bath.
Thereby, a thermodynamic basis is provided for power-law phenomena ubiquitous
in nature.Comment: 12 page
Free-volume kinetic models of granular matter
We show that the main dynamical features of granular media can be understood
by means of simple models of fragile-glass forming liquid provided that gravity
alone is taken into account. In such lattice-gas models of cohesionless and
frictionless particles, the compaction and segregation phenomena appear as
purely non-equilibrium effects unrelated to the Boltzmann-Gibbs measure which
in this case is trivial. They provide a natural framework in which slow
relaxation phenomena in granular and glassy systems can be explained in terms
of a common microscopic mechanism given by a free-volume kinetic constraint.Comment: 4 pages, 6 figure
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