Time Irreversibility Problem and Functional Formulation of Classical Mechanics

Understand

The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics.

• This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some researchers claim that the problem is solved, it deserves a further study.
• In this paper an attempt is performed of the following solution of the irreversibility problem: a formulation of microscopic dynamics is suggested which is irreversible in time.
• A widely used notion of microscopic state of the system at a given moment of time as a point in the phase space and also a notion of trajectory does not have an immediate physical meaning since arbitrary real numbers are non observable.