Lyapunov Exponent of a Many Body System and Its Transport Coefficients

An ab initio theoretical expression for the $N$-body Lyapunov exponent of a dilute gas is derived. It shows the Lyapunov exponent to be a function of the time integral of the correlation function for the second derivative of the interparticle potential (approximately a power $\frac{1}{3}$ law). This establishes a link between the Lyapunov exponent and the transport coefficients. We compare the theory with numerical simulations of a one component plasma.