I make a great, great error, this is an Hamiltonian without kinetic energy, there are only terms in the form

where are reaction velocity equations, is an arbitrary function, and is for example

and the corresponding momentum. The Hamiltonian don’t give more information on the reaction velocities system, it seems only a more compact mode to write the system.

]]>I write only a termine of the Hamiltonian, H(X), because of this term give me the reaction velocity equation, and this dynamics happen for each arbitrary momentum dynamics (the dynamics of can be arbitrary, and one see only the X dynamics).

I must add the term for , and the

others reaction velocity, so that H=H(X)+H(Y)+\cdots, but I wrote a single term like an example.

If I add to the Hamiltonian, this term don’t change the concentration dynamics, like each arbitrary function , but it couild be interesting for the quantization; it is like the Einstein coefficient for the absorption and emissioni of chemical compounds, bit this is only a coarse idea.

Is your idea that the canonically conjugate variables are and some momenta ? Without specifying the canonically conjugate, I can’t work out Hamilton’s equations from your proposed Hamiltonian.

Also: why does your Hamiltonian involve variables and but not or ? There should be complete symmetry between and here.

]]>I think that it is possibile to write a quantum Hamiltonian from the classical Hamiltonian and to obtain an amplitude dynamic for the concentrations

]]>the Hamiltonian of this system is:

So that there is a dynamic equation for the momentum:

if there are invariances of the Hamiltonian, then there are conservation laws.

I am writing on my tablet, so that I cannot be accurate.

]]>Thanks! Most of these corrections will help the final paper, not just the blog articles.

]]>There's still a typo in the last paragraph: ‘can out arise’ should be ‘cannot arise’.

]]>Yes, they are linearly dependent, and this is important!

]]>Yes, sorry!

Thanks for catching that: for some reason typesetting these reactions was difficult, and I did a bit too much cut-and-pasting.

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