Dynamical observables in chaotic systems share the same large deviation rate function when their g functions differ by a 'derived' function, making derived observables have N-independent symmetric distributions.
This may be seen by a direct calcu- lation, ⟨g∗(x)⟩S = Z dxg∗(x)ps(x) = Z dxh(x)ps(x) − Z dxh (f (x)) ps(x)
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Remarkable similarities in distributions of dynamical observables in chaotic systems
Dynamical observables in chaotic systems share the same large deviation rate function when their g functions differ by a 'derived' function, making derived observables have N-independent symmetric distributions.