Fluctuations and the many-body Lyapunov exponent

An ab initio theoretical method is derived for calculating the maximal Lyapunov exponent of an $N$-body system obeying Hamilton's equations. The theory is developed in detail for a dilute gas. It shows the Lyapunov exponent to be a function of the time integral of the correlation function for fluctuations in the second derivative of the interparticle potential (approximately a power $\frac{1}{3}$ law). We apply the theory to a one-component plasma and derive the dependence of the Lyapunov exponent on a plasma parameter.