Fluctuation Theorem and Chaos

TL;DR

This paper explores how the chaotic hypothesis in nonequilibrium thermodynamics leads to the fluctuation theorem, connecting chaos, entropy, and probability distributions in dynamical systems.

Contribution

It establishes a theoretical framework linking the chaotic hypothesis to the fluctuation theorem and the SRB distribution in nonequilibrium thermodynamics.

Findings

Chaotic hypothesis enables unique probability distribution determination.

Fluctuation theorem derived from symmetry properties of SRB distribution.

Unifies foundations of equilibrium and nonequilibrium thermodynamics.

Abstract

The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary states the chaotic hypothesis plays a similar role: it allows a unique determination of the probability distribution (called {\rm SRB} distribution on phase space providing the time averages of the observables. It also implies an expression for a few averages concrete enough to derive consequences of symmetry properties like the fluctuation theorem or to formulate a theory of coarse graining unifying the foundations of equilibrium and of nonequilibrium.