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.

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.

KEYWORDS

Irreversibility, Direct Equations, Reverse Equations, Instability, Multimoment Hydrodynamics

Irreversibility, Direct Equations, Reverse Equations, Instability, Multimoment Hydrodynamics

Cite this paper

Lebed, I. (2014) About Appearance of the Irreversibility.*Open Journal of Fluid Dynamics*, **4**, 298-320. doi: 10.4236/ojfd.2014.43023.

Lebed, I. (2014) About Appearance of the Irreversibility.

References

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http://dx.doi.org/10.4236/ojfd.2013.33027

[4] Lebed, I.V. (1996) Method of Two-Particle Distribution Functions. Hydrodynamic Equations. Chemical Physics Reports, 15, 861-883.

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[6] Lebed, I.V. (1998) About the Behavior of the Entropy of a Gas Flow Losing Its Stability. Chemical Physics Reports, 17, 411-439.

[7] Lebed, I.V. (2014) Development of Instability in the Problem of Flow around a Sphere. Russian Journal of Physical Chemistry B, 8, 240-253.

[8] Lebed, I.V. (2014) Multimoment Hydrodynamics in Problem on Flow around a Sphere: Entropy Interpretation of the Appearance and Development of Instability. Open Journal of Fluid Dynamics, 4, 163-206.

http://dx.doi.org/10.4236/ojfd.2014.42015

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http://dx.doi.org/10.1016/S0378-4371(98)00527-5

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http://dx.doi.org/10.1016/0009-2614(90)85433-D

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http://dx.doi.org/10.1038/051413b0

[24] Boltzmann, L. (1897) Zu Hrn. Zermelo’s Abhandlung “Uber die mechanische Erklarung Irreversibler Vorgangre”. Annalen der Physik, 60, 392-398.

[1] Lebed, I.V. and Umanskii, S.Y. (2007) The Appearance and Development of Turbulence in a Flow Past a Sphere: Problems and the Existing Approaches to Their Solution. Russian Journal of Physical Chemistry B, 1, 52-73.

[2] Lebed, I.V. and Umanskii, S.Y. (2012) On the Possibility of Improving Classic Hydrodynamics Equations by an Increase in the Number of Hydrodynamic Values. Russian Journal of Physical Chemistry B, 6, 149-162.

[3] Lebed, I.V. (2013) About the Prospects for Passage to Instability. Open Journal of Fluid Dynamics, 3, 214-229.

http://dx.doi.org/10.4236/ojfd.2013.33027

[4] Lebed, I.V. (1996) Method of Two-Particle Distribution Functions. Hydrodynamic Equations. Chemical Physics Reports, 15, 861-883.

[5] Lebed, I.V. (1997) The Method of Pair Functions as Applied to the Problem of a Flow around a Quiescent Solid Sphere. Chemical Physics Reports, 16, 1263-1301.

[6] Lebed, I.V. (1998) About the Behavior of the Entropy of a Gas Flow Losing Its Stability. Chemical Physics Reports, 17, 411-439.

[7] Lebed, I.V. (2014) Development of Instability in the Problem of Flow around a Sphere. Russian Journal of Physical Chemistry B, 8, 240-253.

[8] Lebed, I.V. (2014) Multimoment Hydrodynamics in Problem on Flow around a Sphere: Entropy Interpretation of the Appearance and Development of Instability. Open Journal of Fluid Dynamics, 4, 163-206.

http://dx.doi.org/10.4236/ojfd.2014.42015

[9] Lebed, I.V. (1996) Hydrodynamic Equations Stemming from Two Particle Distributions in the Limit of Weak Non-equilibrium. Analysis of Invertibility of Equations. Chemical Physics Reports, 15, 1725-1750.

[10] Einstein, A. and Besso, M. (1972) Correspondence 1903-1955. Hermann, Paris.

[11] Prigogine, I. (1999) Laws of Nature, Probability and Time Symmetry Breaking. Physica A: Statistical Mechanics and Its Applications, 263, 528-539.

http://dx.doi.org/10.1016/S0378-4371(98)00527-5

[12] Liboff, R.L. (1969) Introduction to the Theory of Kinetic Equations. Willey, New York/London/Sydney/Toronto.

[13] Bogolubov, N.N. (1946) The Problems of Dynamic Theory in Statistical Physics. Gostechizdat, Moscow-Leningrad.

[14] Lebed, I.V. (1990) Equations of Pair Distribution Functions. Chemical Physics Letters, 165, 226-228.

http://dx.doi.org/10.1016/0009-2614(90)85433-D

[15] Lebed, I.V. (1995) Derivation of the Equations for Pair Distribution Functions. Chemical Physics Reports, 14, 599-615.

[16] Boltzmann, L. (1896) Entgegnung auf die Warmetheoretischen Betrachtungen des Hrn. Zermelo. Annalen der Physik, 57, 773-784.

[17] Orban, J. and Bellemance, A. (1967) Velocity-Inversion and Irreversibility in a Dilute Gas of Hard Discs. Physics Letters A, 24, 1132-1140.

[18] Lebed, I.V. (1995) Equations for a One-Particle Distribution Function. Chemical Physics Reports, 13, 1132-1140.

[19] Ferziger, J.H. and Kaper, H.G. (1972) Mathematical Theory of Transport Processes in Gases. North-Holland Publishing Company, Amsterdam.

[20] Gibbs, J.W. (1982) Thermodynamics. Statistical Mechanics. Nauka, Moscow.

[21] Zermelo, E. (1896) Uber einen Satz der Dynamik and die mechanische Warmetheorie. Annalen der Physik, 57, 485-494.

[22] Loschmidt, J. (1876) Uber den Zustand des Warmegleichgewichtes eines Systems von Korpern mit Rücksicht auf die Schwerkraft. Wien. Ber., 73, 128-142.

[23] Boltzmann, L. (1894-1895) On Certain Question of the Theory of Gases. Nature, 51, 413-415.

http://dx.doi.org/10.1038/051413b0

[24] Boltzmann, L. (1897) Zu Hrn. Zermelo’s Abhandlung “Uber die mechanische Erklarung Irreversibler Vorgangre”. Annalen der Physik, 60, 392-398.