Stochastic & Chaotic: Examining Evolution

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A stochastic process cannot be considered chaotic due to fundamental differences in their properties. Chaotic systems exhibit deterministic solutions governed by Hamiltonian mechanics, while stochastic systems incorporate random variables, leading to non-deterministic outcomes. The transformation of a deterministic Hamiltonian into one that includes random variables is deemed impossible. This distinction highlights the inherent differences between stochastic and chaotic systems in the context of evolution. Understanding these differences is crucial for accurately examining evolutionary processes.
wathan
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Can we consider a stochastic process being chaotic?

consider evolution of only two particular systems with closed initial states (not ensemble or statistical properties of the system)
 
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Not in general- a 'chaotic' system has specific properties associated with it.
 
The hamiltonian of a stochastic system have a random variable so the solutions of the hamilton equations cannot be deterministic. The hamiltonians of a chaotics systems do not have random variable so the solutions of the hamilton equations are deterministic. You have to transform your deterministic hamiltonian into a hamiltonian with a random variable and I think that is imposible.
 
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