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 & 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), (1974).  doi: 10.1007/978-94-010-2091-6.  Google Scholar

[2]

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

[3]

O. Kupervasser and D. Laikov, Comment on "Quantum solution to the arrow-of-time dilemma",, preprint, ().   Google Scholar

[4]

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

[5]

L. Maccone, A quantum solution to the arrow-of-time dilemma: Reply,, preprint, ().   Google Scholar

[6]

H. Nikolić, Comment on "Quantum solution to the arrow-of-time dilemma",, preprint, ().   Google Scholar

[7]

I. Prigogine, From Being to Becoming,, Freeman, (1980).   Google Scholar

[8]

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

[9]

I. Prigogine and I. Stengers, Order Out of Chaos,, Heinemann, (1984).  doi: 10.1063/1.2813716.  Google Scholar

[10]

I. Prigogine and I. Stengers, Entre le Temps et L'éternité,, Fayard, (1988).   Google Scholar

show all references

References:
[1]

L. Boltzmann, Theoretical Physics and Philosophical Problems,, selected writings (ed. B. McGuinness), (1974).  doi: 10.1007/978-94-010-2091-6.  Google Scholar

[2]

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

[3]

O. Kupervasser and D. Laikov, Comment on "Quantum solution to the arrow-of-time dilemma",, preprint, ().   Google Scholar

[4]

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

[5]

L. Maccone, A quantum solution to the arrow-of-time dilemma: Reply,, preprint, ().   Google Scholar

[6]

H. Nikolić, Comment on "Quantum solution to the arrow-of-time dilemma",, preprint, ().   Google Scholar

[7]

I. Prigogine, From Being to Becoming,, Freeman, (1980).   Google Scholar

[8]

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

[9]

I. Prigogine and I. Stengers, Order Out of Chaos,, Heinemann, (1984).  doi: 10.1063/1.2813716.  Google Scholar

[10]

I. Prigogine and I. Stengers, Entre le Temps et L'éternité,, Fayard, (1988).   Google Scholar

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