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For instance, take the following macrostate as an example,

- T = 0

- V = v, dV/dt = 0

- P = p, dP/dt = 0

Indeed the microstate describing this macrostate is unique in quadratic terms (the momentum of every particle must be zero). But it does not seem to be unique in the first-order terms - I can shuffle the positions of the particles all I want and keep producing the same macrostate.

So, by formal definition,

**is entropy**

*only*affected by quadratic and higher order terms of the Hamiltonian of the N particles contributing to the macrostate?