Abstract
The Heat theorem reveals the second law of Thermodynamics as a manifestation of a
general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as wel l as
1023 degrees of freedom systems, i.e. for simple as wel l as very complex systems, and reflecting
the symplectic symmetry. In Nonequilibrium Thermodynamics it does not seem that there are
theorems of comparable generality. Yet it is possible to find general, model independent, properties
valid even for simple chaotic systems (i.e. the hyperbolic ones), which acquire special interest for
larger systems: the Chaotic Hypothesis leads to the Fluctuation Theorem which provides general
properties of very large fluctuations and reflects the time-reversal symmetry.
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