On the arrow of time

Previous Article
Stoichiometric producer-grazer models with varying nitrogen pools and ammonia toxicity
DCDS-S Home
This Issue
Next Article
Dynamics of two phytoplankton species competing for light and nutrient with internal storage

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

On the arrow of time

Y. Charles Li ^1, and Hong Yang ^2,

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

Abstract
Related Papers

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.

Keywords: chaos, Arrow of time, Poincaré recurrence theorem, ergodicity..

Mathematics Subject Classification: Primary: 82; Secondary: 3.

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, ().
[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, ().
[6]	H. Nikolić, Comment on "Quantum solution to the arrow-of-time dilemma",, preprint, ().
[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, ().
[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, ().
[6]	H. Nikolić, Comment on "Quantum solution to the arrow-of-time dilemma",, preprint, ().
[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.

[1]	Jean René Chazottes, F. Durand. Local rates of Poincaré recurrence for rotations and weak mixing. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 175-183. doi: 10.3934/dcds.2005.12.175
[2]	Chihurn Kim, Dong Han Kim. On the law of logarithm of the recurrence time. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 581-587. doi: 10.3934/dcds.2004.10.581
[3]	William Clark, Anthony Bloch, Leonardo Colombo. A Poincaré-Bendixson theorem for hybrid systems. Mathematical Control and Related Fields, 2020, 10 (1) : 27-45. doi: 10.3934/mcrf.2019028
[4]	Piotr Oprocha. Chain recurrence in multidimensional time discrete dynamical systems. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1039-1056. doi: 10.3934/dcds.2008.20.1039
[5]	Armengol Gasull, Víctor Mañosa. Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 651-670. doi: 10.3934/dcdsb.2019259
[6]	D. P. Demuner, M. Federson, C. Gutierrez. The Poincaré-Bendixson Theorem on the Klein bottle for continuous vector fields. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 495-509. doi: 10.3934/dcds.2009.25.495
[7]	Julián López-Gómez, Eduardo Muñoz-Hernández, Fabio Zanolin. On the applicability of the poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2393-2419. doi: 10.3934/dcds.2020119
[8]	Denis Blackmore, Jyoti Champanerkar, Chengwen Wang. A generalized Poincaré-Birkhoff theorem with applications to coaxial vortex ring motion. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 15-33. doi: 10.3934/dcdsb.2005.5.15
[9]	Olivier P. Le Maître, Lionel Mathelin, Omar M. Knio, M. Yousuff Hussaini. Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 199-226. doi: 10.3934/dcds.2010.28.199
[10]	Dmitry Turaev, Sergey Zelik. Analytical proof of space-time chaos in Ginzburg-Landau equations. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1713-1751. doi: 10.3934/dcds.2010.28.1713
[11]	José Miguel Pasini, Tuhin Sahai. Polynomial chaos based uncertainty quantification in Hamiltonian, multi-time scale, and chaotic systems. Journal of Computational Dynamics, 2014, 1 (2) : 357-375. doi: 10.3934/jcd.2014.1.357
[12]	E.V. Presnov, Z. Agur. The Role Of Time Delays, Slow Processes And Chaos In Modulating The Cell-Cycle Clock. Mathematical Biosciences & Engineering, 2005, 2 (3) : 625-642. doi: 10.3934/mbe.2005.2.625
[13]	Petr Kůrka, Vincent Penné, Sandro Vaienti. Dynamically defined recurrence dimension. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 137-146. doi: 10.3934/dcds.2002.8.137
[14]	Serge Troubetzkoy. Recurrence in generic staircases. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 1047-1053. doi: 10.3934/dcds.2012.32.1047
[15]	Michael Blank. Recurrence for measurable semigroup actions. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1649-1665. doi: 10.3934/dcds.2020335
[16]	Michel Benaim, Morris W. Hirsch. Chain recurrence in surface flows. Discrete and Continuous Dynamical Systems, 1995, 1 (1) : 1-16. doi: 10.3934/dcds.1995.1.1
[17]	Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1
[18]	Milton Ko. Rényi entropy and recurrence. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2403-2421. doi: 10.3934/dcds.2013.33.2403
[19]	Miguel Abadi, Sandro Vaienti. Large deviations for short recurrence. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 729-747. doi: 10.3934/dcds.2008.21.729
[20]	Ali Gholami, Mauricio D. Sacchi. Time-invariant radon transform by generalized Fourier slice theorem. Inverse Problems and Imaging, 2017, 11 (3) : 501-519. doi: 10.3934/ipi.2017023

2020 Impact Factor: 2.425

Tools

Metrics

Other articles
by authors

on AIMS
Y. Charles Li Hong Yang
on Google Scholar
Y. Charles Li Hong Yang

[Back to Top]