  The uniformly hyperbolic Anosov C-systems defined on a torus have exponential
instability of their trajectories, and as such C-systems have mixing of all
orders and nonzero Kolmogorov entropy. The mixing property of all orders means
that all its correlation functions tend to zero and the question of a
fundamental interest is a speed at which they tend to zero. It was proven that
the speed of decay in the C-systems is exponential, that is, the observables on
the phase space become independent and uncorrelated exponentially fast. It is
important to specify the properties of the C-system which quantify the
exponential decay of correlations. We have found that the upper bound on the
exponential decay of the correlation functions universally depends on the value
of a system entropy. A quintessence of the analyses is that local and
homogeneous instability of the C-system phase space trajectories translated
into the exponential decay of the correlation functions at the rate which is
proportional to the Kolmogorov entropy, one of the fundamental characteristics
of the Anosov automorphisms. This result allows to define the decorrrelation
and relaxation times of a C-system in terms of its entropy and characterise the
statistical properties of a broad class of dynamical systems, including
pseudorandom number generators and gravitational systems.
