December  2014, 7(6): 1287-1303. doi: 10.3934/dcdss.2014.7.1287

On the arrow of time

1. 

Department of Mathematics, University of Missouri, Columbia, MO 65211, United States

2. 

Mathematics of Networks and Communications Research Department, Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, United States

Received  January 2013 Revised  August 2013 Published  June 2014

We believe the following three ingredients are enough to explain the mystery of the arrow of time: (1). equations of dynamics of gas molecules, (2). chaotic instabilities of the equations of dynamics, (3). unavoidable perturbations to the gas molecules. The level of physical rigor or mathematical rigor that can be reached for such a theory is unclear.
Citation: Y. Charles Li, Hong Yang. On the arrow of time. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1287-1303. doi: 10.3934/dcdss.2014.7.1287
References:
[1]

L. Boltzmann, Theoretical Physics and Philosophical Problems, selected writings (ed. B. McGuinness), Vienna Circle Collection, 5, Springer Netherlands, 1974, p. 204. doi: 10.1007/978-94-010-2091-6.

[2]

D. Jennings and T. Rudolph, Comment on "Quantum solution to the arrow-of-time dilemma", Physical Review Letters, 104 (2010), 148901. doi: 10.1103/PhysRevLett.104.148901.

[3]

O. Kupervasser and D. Laikov, Comment on "Quantum solution to the arrow-of-time dilemma", preprint, arXiv:0911.2610.

[4]

L. Maccone, Quantum solution to the arrow-of-time dilemma, Physical Review Letters, 103 (2009), 080401, 4 pp. doi: 10.1103/PhysRevLett.103.080401.

[5]

L. Maccone, A quantum solution to the arrow-of-time dilemma: Reply, preprint, arXiv:0912.5394.

[6]

H. Nikolić, Comment on "Quantum solution to the arrow-of-time dilemma", preprint, arXiv:0912.1947.

[7]

I. Prigogine, From Being to Becoming, Freeman, New York, 1980.

[8]

I. Prigogine, Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems, Int. J. Quantum Chemistry, 5 (1995), 3-16. doi: 10.1142/S0218127495000028.

[9]

I. Prigogine and I. Stengers, Order Out of Chaos, Heinemann, London, 1984. doi: 10.1063/1.2813716.

[10]

I. Prigogine and I. Stengers, Entre le Temps et L'éternité, Fayard, Paris, 1988.

show all references

References:
[1]

L. Boltzmann, Theoretical Physics and Philosophical Problems, selected writings (ed. B. McGuinness), Vienna Circle Collection, 5, Springer Netherlands, 1974, p. 204. doi: 10.1007/978-94-010-2091-6.

[2]

D. Jennings and T. Rudolph, Comment on "Quantum solution to the arrow-of-time dilemma", Physical Review Letters, 104 (2010), 148901. doi: 10.1103/PhysRevLett.104.148901.

[3]

O. Kupervasser and D. Laikov, Comment on "Quantum solution to the arrow-of-time dilemma", preprint, arXiv:0911.2610.

[4]

L. Maccone, Quantum solution to the arrow-of-time dilemma, Physical Review Letters, 103 (2009), 080401, 4 pp. doi: 10.1103/PhysRevLett.103.080401.

[5]

L. Maccone, A quantum solution to the arrow-of-time dilemma: Reply, preprint, arXiv:0912.5394.

[6]

H. Nikolić, Comment on "Quantum solution to the arrow-of-time dilemma", preprint, arXiv:0912.1947.

[7]

I. Prigogine, From Being to Becoming, Freeman, New York, 1980.

[8]

I. Prigogine, Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems, Int. J. Quantum Chemistry, 5 (1995), 3-16. doi: 10.1142/S0218127495000028.

[9]

I. Prigogine and I. Stengers, Order Out of Chaos, Heinemann, London, 1984. doi: 10.1063/1.2813716.

[10]

I. Prigogine and I. Stengers, Entre le Temps et L'éternité, Fayard, Paris, 1988.

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