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Entropy of deterministic trajectory via trajectories ensemble |
| Yonggang Peng(彭勇刚)†, Cuiping Ran(冉翠平), and Yujun Zheng(郑雨军)‡ |
| School of Physics, Shandong University, Jinan 250100, China |
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Abstract We present a formulation of the single-trajectory entropy using the trajectories ensemble. The single-trajectory entropy is affected by its surrounding trajectories via the distribution function. The single-trajectory entropies are studied in two typical potentials, i.e., harmonic potential and double-well potential, and in viscous environment by interacting trajectory method. The results of the trajectory methods are in agreement well with the numerical methods (Monte Carlo simulation and difference equation). The single-trajectory entropies increasing (decreasing) could be caused by absorption (emission) heat from (to) the thermal environment. Also, some interesting trajectories, which correspond to the rare evens in the processes, are demonstrated.
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Received: 03 January 2024
Revised: 06 March 2024
Accepted manuscript online: 13 March 2024
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PACS:
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34.10.+x
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(General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.))
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 12234013) and the Natural Science Foundation of Shandong Province (Grant No. ZR2021LLZ009). |
Corresponding Authors:
Yonggang Peng, Yujun Zheng
E-mail: ygpeng@sdu.edu.cn;yzheng@sdu.edu.cn
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Cite this article:
Yonggang Peng(彭勇刚), Cuiping Ran(冉翠平), and Yujun Zheng(郑雨军) Entropy of deterministic trajectory via trajectories ensemble 2024 Chin. Phys. B 33 063401
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[1] Lemons D S 2013 A Student’s Guide to Entropy (Cambridge: Cambridge University Press)
[2] Attard P 2002 Thermodynamics and Statistical Mechanics: Equilibrium by Entropy Maximisation (Cornwa: Academic Press)
[3] Sachs I, Sen S and Sexton J 2006 Elements of Statistical Mechanics (Cambridge: Cambridge University Press)
[4] Wehrl A 1978 Rev. Mod. Phys. 50 221
[5] Huang K 1987 Statistical Mechanics 2nd Edn. (New York: Wiley)
[6] Chandler D 1987 Introduction to Modern Statistical Mechanics (Oxford: Oxford University Press)
[7] Gibbs J W 1960 Elementary Principles in Statistical Mechanics (New York: Dover Publications)
[8] Jaynes E T 1965 Am. J. Phys. 33 391
[9] Zupanovic P and Kuic D 2018 J. Phys. Commun. 2 045002
[10] Shannon C E 1948 Bell System Tech. J. 27 379
[11] von Neumann J 1955 The Mathematical Foundations of Quantum Mechanics (Princeton: Princeton University Press)
[12] Haas K R, Yang H and Chu J W 2014 J. Phys. Chem. B 118 8099
[13] Haas K R, Yang H and Chu J W 2014 J. Phys. Chem. Lett. 5 999
[14] Weiderpass G A and Caldeira A O 2020 Phys. Rev. E 102 032102
[15] Rossi M, Mancino L, Landi G T and Paternostro M 2020 Phys. Rev. Lett. 125 080601
[16] Klages R, Just W and Jarzynski C (eds) 2013 Nonequilibrium Statistical Physics of Small Systems (Weinheim: Wiley-VCH Verlag)
[17] Holian B L 1986 Phys. Rev. A 33 1152
[18] Grandy and Jr W T 2008 Entropy and the Time Evolution of Macroscopic Systems (New York: Oxford University Press)
[19] Kleidon A and Lorenz R D (eds) 2005 Non-Equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond (Berlin: Springer-Verlag)
[20] Seifert U 2012 Rep. Prog. Phys. 75 126001
[21] Sekimoto K 1998 Prog. Theor. Phys. Suppl. 130 17
[22] Evans D J, Cohen E G D and Morriss G P 1993 Phys. Rev. Lett. 71 2401
[23] Evans D J and Searles D J 1994 Phys. Rev. E 50 1645
[24] Gallavotti G and Cohen E G D 1995 Phys. Rev. Lett. 74 2694
[25] Seifert U 2005 Europhys. Lett. 70 36
[26] Kurchan J 1998 J. Phys. A: Math. Gen. 31 3719
[27] Jarzynski C 1997 Phys. Rev. Lett. 78 2690
[28] Crooks G E 1999 Phys. Rev. E 60 2721
[29] Hatano T and Sasa S i 2001 Phys. Rev. Lett. 86 3463
[30] Qian M 1985 Chin. Sci. Bull. 30 165 (in Chinese)
[31] Seifert U 2005 Phys. Rev. Lett. 95 040602
[32] Tietz C, Schuler S, Speck T, Seifert U and Wrachtrup J 2006 Phys. Rev. Lett. 97 050602
[33] Mandal D, Klymko K and DeWeese M R 2017 Phys. Rev. Lett. 119 258001
[34] Bunker D L 1971 Methods Comput. Physics: Adv. Res. Appl. 10 287
[35] Sanz A S and Miret-Artes S 2012 A Trajectory Description of Quantum Processes (Berlin: Springer)
[36] Chattaraj P K (ed) 2010 Quantum Trajectories (Boca Raton: CRC Press)
[37] Wyatt R E and Trahan C J 2005 Quantum Dynamics with Trajectories (Berlin: Springer)
[38] Donoso A and Martens C C 2001 Phys. Rev. Lett. 87 223202
[39] Donoso A and Martens C C 2002 J. Chem. Phys. 116 10598
[40] Sun Z, Dong H and Zheng Y 2018 Phys. Rev. E 97 012132
[41] Xu F, Martens C C and Zheng Y 2017 Phys. Rev. A 96 022138
[42] Wang L, Martens C C and Zheng Y 2012 J. Chem. Phys. 137 034113
[43] Attard P 2012 Non-Equilibrium Thermodynamics and Statistical Mechanics (Oxford: Oxford University Press)
[44] Brewster R A and Frason J D 2018 J. Math. Phys. 59 012102
[45] Wand M P and Jones M C 1995 Kernel Smoothing (New York: Springer)
[46] Silverman B W 1998 Density Estimation for Statistics and Data Analysis (New York: Chapman & Hall)
[47] Kramers H A 1940 Physica 7 284
[48] Kubo R, TodaMand hashitsume N 1985 Statistical Physics II: Nonequilibrium Statistical Mechanics (Berlin: Springer-Verlag)
[49] Gardiner C W 2004 Handbook of Stochastic Methods 3rd Edn. (Berlin: Springer-Verlag)
[50] van Kampen N G 2007 Stochastic Processes in Physics and Chemistry 3rd edn (Singapore: Elsevier)
[51] Risken H 1996 The Fokker-Planck Equation 2nd Edn. (Berlin: Springer-Verlag)
[52] Jacobs K 2010 Stochastic Processes for Physicists - Understanding Noisy Systems (Cambridge: Cambridge University Press) |
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