** Archivi** FM 10-07, mp_arc 07-283 , cond-mat/07-2755

** Author** Giovanni Gallavotti

** Title ***Heat and Fluctuations from Order to Chaos*

** Abstract **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 $10^{23}$ 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. The paper is written taking some care that each section
and appendix is readable either independently of the rest or with
only few cross references.

** Keywords ** Nonequilibrium Statistical Mechanics, Chaotic
Hypothesis, Fluctuation Theorem, Entropy, Large Deviations, Quantum
Nonequilibrium, Thermostats

Giovanni
Gallavotti
Last modified: Sat Nov 17 20:19:44 CET 2007