Chaos-transport formula

C. The Chaos-Transport Formula Time Asymmetry in Dynamical Randomness A. Randomness of Fluctuations in NonequiUbrium Steady States... 

Figure 13. Diagram showing how dynamical instability characterized by the sum of positive Lyapunov exponents > o contributes to dynamical randomness characterized by the Kolmogorov-Sinai entropy per unit time h s and to the escape y due to transport according to the chaos-transport formula (95).

This form shows the deep similarity with the chaos-transport formula (95) and Eq. (101). 

We notice the similarity of the structures of Eq. (101) with the chaos-transport relationship (95). Indeed, both formulas are large-deviation dynamical relationships giving an irreversible property from the difference between two quantities characterizing the dynamical randomness or instability of the microscopic dynamics (see Fig. 16). 

If we combine the escape-rate formula (92) with the result (84) that the escape rate is proportional to the transport coefficient, we obtain the following large-deviation relationships between the transport coefficients and the characteristic quantities of chaos [37, 39] ... 

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