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In recent years, the property of nonequilibrium thermodynamics in closed system, especially in spin chain system undergoing a quenching process, has become one of the hot topics in the quantum thermodynamics. The nonequilibrium thermodynamic properties of XY spin chain with XZX + YZY type of three-site interaction under a transverse field are studied by considering an exactly solvable model. First we review some basic concepts, i.e., the work distribution, the averaged work, the fluctuation of work, and the irreversible entropy in the nonequilibrium thermodynamics, and give the theoretical model and its solutions. Then, we concretely discuss the effects of the three-site interaction of XZX + YZY type on the average work, the fluctuation of work and the irreversible entropy in the extended XY chain undergoing a quench process. The theoretical calculation and numerical simulation show that the three-site interaction of XZX + YZY type may play a positive and negative role in the increase of the averaged work, which depends on the strength of initial external magnetic field. Moreover, we also find that work fluctuation can be effectively suppressed by adjusting the intensity of XZX + YZY three-site interaction. Finally, it is found that the irreversible entropy production presents a sharp peak characteristic near the critical magnetic field, and the value of the peak sharp decreases with the increase of XZX + YZY three-site interaction. Simultaneously, the corresponding physical explanations are also given. In a word, the results given in present paper may increasingly arouse one’s interest in the nonequilibrium quantum thermodynamics.
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Keywords:
- XY spin chain with multisite interaction /
- averaged work /
- fluctuation of work /
- irreversible entropy production
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图 2 平均功
$\left\langle W \right\rangle$ 在不同的三格点相互作用强度$\alpha$ 和各向异性参数$\gamma $ 下随初始外磁场强度$\lambda _0$ 的变化 (a)$\gamma = 0.1$ ; (b)$\gamma = 0.8$ ; 其他的参数被设定为$\beta = 100$ ,$ \text {δ} \lambda = \lambda _\tau - \lambda _0 = 0.01$ ,$N = 5000$ Figure 2. Averaged work
$\left\langle W \right\rangle$ and work distribution fluctuation$\varSigma ^2$ as a function of$\lambda _0$ under various$\alpha$ for$\gamma = 0.1 $ (a) and$\gamma = 0.8$ (b). Other parameters are$\beta = 100$ ,$ \text{δ} \lambda = \lambda _\tau - \lambda _0 = 0.01$ and$N = 5000$ .
图 3 功涨落
$\varSigma ^2$ 对于不同的三格点相互作用强度$\alpha$ 和各向异性参数$\gamma $ 随初始外磁场强度$\lambda _0$ 的变化 (a)$\gamma = 0.1$ ; (b)$\gamma = 0.8$ ; 其他的参数被设定为$\beta = 100$ ,$ \text{δ} \lambda = \lambda _\tau - \lambda _0 = 0.01$ ,$N = 5000$ Figure 3. Work fluctuation
$\varSigma ^2$ as a function of$\lambda _0$ under various$\alpha$ for$\gamma = 0.1$ (a) and$\gamma = 0.8$ (b). Other parameters are$\beta = 100,$ $ \text{δ} \lambda = \lambda _\tau - \lambda _0 = 0.01$ and$N = 5000$ .
图 4 不可逆熵产生
$\Delta S_{{\rm{irr}}}$ 对于不同的三格点相互作用强度$\alpha$ 和各向异性参数$\gamma $ 随初始外磁场强度$\lambda _0$ 的变化 (a)$\gamma = 0.1$ ; (b)$\gamma = 0.8$ ; 其他的参数被设定为$\beta = 100$ ,$ {\text{δ}} \lambda = \lambda _\tau - \lambda _0 = 0.01$ ,$N = 5000$ Figure 4. Irreversible entropy production
$\Delta S_{{\rm{irr}}}$ as a function of$\lambda _0$ under various$\alpha$ for$\gamma = 0.1$ (a) and$\gamma = 0.8$ (b). Other parameters are$\beta = 100$ ,$ {\text{δ}} \lambda = \lambda _\tau - \lambda _0 = 0.01$ and$N = 5000$ . -
[1] Greiner M, Mandel O, Hansch T W, Bloch I 2002 Nature 419 51
Google Scholar
[2] Kinoshita T, Wenger T, Weiss D S 2006 Nature 440 900
Google Scholar
[3] Bloch I, Dalibard J, Wenger W 2008 Rev. Mod. Phys. 80 885
Google Scholar
[4] Jarzynski C 1997 Phys. Rev. Lett. 78 2690
Google Scholar
[5] Crooks G E 1999 Phys. Rev. E 60 2721
Google Scholar
[6] Talkner P, Hanggi P 2007 J. Phys. A 40 F569
Google Scholar
[7] Talkner P, Lutz E, Hanggi P 2007 Phys. Rev. E 75 050102(R)
Google Scholar
[8] Esposito M, Harbola U, Mukamel S 2009 Rev. Mod. Phys. 81 1665
Google Scholar
[9] Sagawa T, Ueda M 2010 Phys. Rev. Lett. 104 090602
Google Scholar
[10] Campisi M, Hanggi P, Talkner P 2011 Rev. Mod. Phys. 83 771
Google Scholar
[11] Seifert U 2012 Rep. Prog. Phys. 75 126001
Google Scholar
[12] Huber G, Kaler F S, Deffner S, Lutz E 2008 Phys. Rev. Lett. 101 070403
Google Scholar
[13] Dorner R, Clark S R, Heaney L, Fazio R, Goold J, Vedral V 2013 Phys. Rev. Lett. 110 230601
Google Scholar
[14] Mazzola L, De Chiara G, Paternostro M 2013 Phys. Rev. Lett. 110 230602
Google Scholar
[15] An S, Zhang J N, Um M, Lv D, Lu Y, Zhang J, Yin Z Q, Quan H T 2015 Nat. Phys. 11 193
Google Scholar
[16] Xiong T P, Yan L L, Zhou F, Rehan K, Liang D F, Chen L, Yang W L, Ma Z H, Feng M, Vedral V 2018 Phys. Rev. Lett. 120 010601
Google Scholar
[17] Silva A 2008 Phys. Rev. Lett. 101 120603
Google Scholar
[18] Dorner R, Goold J, Cormick C, Paternostro M, Vedral V 2012 Phys. Rev. Lett. 109 160601
Google Scholar
[19] Bayocboc F A, Paraan F N C 2015 Phys. Rev. E 92 032142
Google Scholar
[20] Zhong M, Tong P Q 2015 Phys. Rev. E 91 032137
Google Scholar
[21] Wang Q, Cao D, Quan H T 2018 Phys. Rev. A 98 022107
Google Scholar
[22] Xu B M, Zou J, Guo L S, Kong X M 2018 Phys. Rev. A 97 052122
Google Scholar
[23] Roger M, Hetherington J H, Delrieu J M 1983 Rev. Mod. Phys. 55 1
Google Scholar
[24] Titvinidze I, Japaridze G I 2003 Eur. Phys. J. B 32 383
Google Scholar
[25] Cheng W W, J M Liu 2010 Phys. Rev. A 81 044304
Google Scholar
[26] Cheng W W, J M Liu 2010 Phys. Rev. A 82 012308
Google Scholar
[27] Lian H L 2011 Physica B 406 4278
Google Scholar
[28] 单传家 2012 物理学报 61 220302
Google Scholar
Shan C J 2012 Acta Phys. Sin. 61 220302
Google Scholar
[29] 郗玉兴, 单传家, 黄燕霞 2014 物理学报 63 110305
Google Scholar
Xi Y X, Shan C J, Huang Y X 2014 Acta Phys. Sin. 63 110305
Google Scholar
[30] Deffner S, Lutz E 2010 Phys. Rev. Lett. 105 170402
Google Scholar
[31] Donald M J 1987 J. Stat. Phys. 49 81
Google Scholar
[32] Sachdev S 1999 Quantum Phase Transitions (Cambridge: Cambridge University) pp 61−64
[33] Zhang J, Shao B, Zou J, Li Q S 2011 Chin. Phys. B 20 100307
Google Scholar
[34] Zhang A P, Li F L 2013 Chin. Phys. B 22 030308
Google Scholar
[35] Quan H T, Song Z, Liu Y X, Zanardi P, Sun C P 2006 Phys. Rev. Lett. 96 140604
Google Scholar
[36] Yuan Z G, Zhang P, Li S S 2007 Phys. Rev. A 75 012102
Google Scholar
[37] Prosen T, Seligman T H, Znidaric M 2003 Prog. Theor. Phys. Suppl. 150 200
Google Scholar
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