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In both classical and quantum mechanics knowledge of the present state of an isolated system allows it's future state to be calculated. If yes then why if not then why ?

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yes and no: it is possible to find chaos from some starting conditions for a physical system and predictable behaviour from others. It is a huge subject. In a physical system an example is double and triple pendulums and in a chemical one the Schlogl equations, $\ce{Y +2X= 3X; Z = X}$ . See 'From Calculus to Chaos' by D. Acheson (Publ OUP) and Nonlinear Dynamics and Chaos, by S. Strogatz (Westview Press) for many examples, including the Lorenz equations, turbulence and forced oscillations. The Poincare-Bendixon theorem is used to predict when chaos will occur and when it will not.

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