Nonunitary transformations and hydrodynamic limit in the one-dimensional hard-point gas (Q1116798)

The ergodic-theoretical formalism of nonunitary ``\(\Lambda\) '' transformations is compared with the derivation of kinetic equations by the hydrodynamic scaling limit. The one-dimensional hard-point system is used as an illustration. Both methods rest on the K-mixing property of the physical systems considered. We show that the specific form of the operator \(\Lambda\) is important only on the microscopic time scale: on the macroscopic scale, it acts like a projector (with broken time- reversal symmetry). We also discuss the connection between the Kolmogorov-Sinai entropy of the model dynamical system, the relative entropy production rate in the nonunitary formalism and the macroscopic entropy production rate.