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Heat and Fluctuations from Order to Chaos
The Heat theorem reveals the second law of equilibrium Thermodynamics
(i.e.existence of Entropy) as a manifestation of a general property of
Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as
degrees of freedom systems, {\it i.e.} for simple as well as very
complex systems, and reflecting the Hamiltonian nature of the microscopic
motion. In Nonequilibrium Thermodynamics theorems of comparable generality do
not seem to be available. Yet it is possible to find general, model
independent, properties valid even for simple chaotic systems ({\it i.e.} the
hyperbolic ones), which acquire special interest for large systems: the Chaotic
Hypothesis leads to the Fluctuation Theorem which provides general properties
of certain very large fluctuations and reflects the time-reversal symmetry.
Implications on Fluids and Quantum systems are briefly hinted. The physical
meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation
Theorem is discussed in the context of their interpretation and relevance in
terms of Coarse Grained Partitions of phase space. This review is written
taking some care that each section and appendix is readable either
independently of the rest or with only few cross references.Comment: 1) added comment at the end of Sec. 1 to explain the meaning of the
title (referee request) 2) added comment at the end of Sec. 17 (i.e. appendix
A4) to refer to papers related to the ones already quoted (referee request
Path Integral Monte Carlo study of phonons in the bcc phase of He
Using Path Integral Monte Carlo and the Maximum Entropy method, we calculate
the dynamic structure factor of solid He in the bcc phase at a finite
temperature of T = 1.6 K and a molar volume of 21 cm. Both the
single-phonon contribution to the dynamic structure factor and the total
dynamic structure factor are evaluated. From the dynamic structure factor, we
obtain the phonon dispersion relations along the main crystalline directions,
[001], [011] and [111]. We calculate both the longitudinal and transverse
phonon branches. For the latter, no previous simulations exist. We discuss the
differences between dispersion relations resulting from the single-phonon part
vs. the total dynamic structure factor. In addition, we evaluate the formation
energy of a vacancy.Comment: 10 figure
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