Abstract: A connection between thermodynamics and dynamical systems is made
by recognizing that any three dimensional evolutionary vector field has a Jacobian matrix which always satisfies a Cayley-Hamilton cubic polynomial. By expressing this polynomial in terms of coordinates composed from the similarity invariants of the matrix, a correspondence can be made to a universal Gibbs surface of van der Waals gas. It is possible to determine the critical point, the Spinodal line representing the limit of thermodynamic stability, and the ''mixed phase'' region for any dynamical system.

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