Extended nonequilibrium systems can be studied in the framework of field theory or from the dynamical systems perspective. Here we report numerical evidence that the sum of a well-defined number of instantaneous Lyapunov exponents for the complex Ginzburg-Landau equation is given by a simple function of the space average of the square of the macroscopic field. This relationship follows from an explicit formula for the time-dependent values of almost all the exponents.