This contribution describes how conservative
time reversible Kolmogorov systems which are some of the most unstable systems currently
known in chaos theory allow for the construction of equivalent irreversible dissipative
systems by means of a necessarily non-unitary but invertible transformation. This
transformation is derived as an operator based on the notion of internal time of the
system under consideration which relates entropy to age and essentially implements a
convolution operation in an adequately chosen set of basis functions.
As an application we mention the field of cryptography. It will be shown how Kolmogorov
systems can be utilized to implement highly efficient computationally secure ciphers for
bulk encryption applications. The highly unstable dynamics associated with Kolmogorov
systems is thereby taken as a chaotic nonlinear permutation operator, while substitution
is implemented using an adaption of a standard shift register based pseudo random number
generator.