About Appearance of the Irreversibility

Abstract

The inevitability of arising in equations of kinetics and hydrodynamics irreversibility not contained in original equations of classic mechanics is substantiated. It is established that transfer of information about the direction of system evolution from initial conditions to resulting equations is the consequence of losing information about the position of an individual particle in space, which takes place at roughening description. It is shown that the roughening with respect to impact parameters of colliding particles is responsible for appearance of the irreversibility in resulting equations. Direct equations of kinetics and hydrodynamics are the result of roughening distribution functions with respect to impact parameters of particles, which have not yet reached the domain of their interaction. The direct equations are valid for the progressive direction of timing on the time axis pointing from the past to the future. Reverse equations of kinetics and hydrodynamics are the result of roughening distribution functions with respect to impact parameters of particles, which have already left the domain of their interaction. The reverse equations are valid for the progressive direction of timing on the time axis pointing from the future to the past.

Kinetic Foundation for the Multimoment Hydrodynamics Equations

“…This is information about mutual disposition of particles in the pair contained in the app p F dependence on b and ε . According to [17], in order to proceed to the kinetic stage, we replace this function by its average value:…”

Derivation of the Multimoment Hydrodynamics Equations for a Gas Mixture

“…The physical meaning of operation (4.7) was disclosed by Lebed (2014c). Introduce the operation (3.7) of space averaging of functions in Equation (4.6).…”

“…According to Lebed (2014c), in order to proceed to the kinetic stage, we replace this function by its average value,…”

“…This is information about mutual disposition of particles in the pair contained in the ( , ) app p i j F dependence on b and ε . According to Lebed (2014c), in order to proceed to the kinetic stage, we replace this function by its average value, ( , ) ( , ) 2 1 ( , , , ' , , ) ( , , , ' ) =…”

“…They are the disintegration of the Gibbs ensemble (Lebed, 1997;2014b), the breakage of unstable solution (Lebed, 1997;2014b), the movement of a system at an extremely unlikely direction described by the reverse multimoment hydrodynamics equations (Lebed, 2014b;2014c;2015b).It was discovered that system entropy begins to play the key role to predict the direction of instability development. The calculation of the system evolution becomes impossible without participation of the entropy.…”