Publications
2020
  • Wenshen Song, Ruixiang Fei, Linghan Zhu, and Li Yang, "Nonreciprocal second-harmonic generation in few-layer chromium triiodide", Phys. Rev. B 102, 045411 (2020).
  • Linghan Zhu and Li Yang, "Quasiparticle energies and excitonic effects of chromium trichloride: From two dimensions to bulk", Phys. Rev. B (editor's suggestion) 101, 245401 (2020).
  • Jing-Kai Qin, Pai-Ying Liao, Mengwei Si, Shiyuan Gao, Gang Qiu, Jie Jian, Qingxiao Wang, Si-Qi Zhang, Shouyuan Huang, Adam Charna, Yixiu Wang, Moon Kim, Wenzhuo Wu, Xianfan Xu, Hai-Yan Wang, Li Yang, Yoke Khin Yap, and Peide Ye, "Raman response and transport properties of tellurium atomic chains encapsulated in nanotubes", Nature Electronics 3, 141 (2020).
  • Wenshen Song, Guang-Yu Guo, Su Huang, Lan Yang, and Li Yang, "First-principles Studies of Second-Order Nonlinear Optical Properties of Organic-Inorganic Hybrid Halide Perovskites", Phys. Rev. Appl. 13, 014052 (2020).
  • Yan Lu, Ruixiang Fei, Xiaobo Lu, Linghan Zhu, Li Wang, and Li Yang, "Artificial Multiferroics and Enhanced Magnetoelectric Effect in van der Waals Heterostructures", ACS Appl. Mater. Interfaces 12, 6243 (2020).
  • Chen Chen, Xiaobo Lu, Bingchen Deng, Xiaolong Chen, Qiushi Guo, Cheng Li, Chao Ma, Shaofan Yuan, Eric Sung, Kenji Watanabe, Takashi Taniguchi, Li Yang, and Fengnian Xia, "Widely tunable mid-infrared light emission in thin-film black phosphorus", Science Adv. 6, eaay6134 (2020).
  • Xiaopeng Fan, Zhurun Ji, Ruixiang Fei, Weihao Zheng, Wenjing Liu, Xiaoli Zhu, Shula Chen, Li Yang, Hongjun Liu, Anlian Pan, and Ritesh Agarwal, "Mechanism of Extreme Optical Nonlinearities in Spiral WS2 above the Bandgap", Nano Lett. 20, 2667 (2020).
2019
  • Yingzhen Tian, Weiwei Gao, Erik Henriksen, James Chelikowsky, Li Yang, "Optically Driven Magnetic Phase Transition of Monolayer RuCl3", Nano Lett. 19, 7673 (2019).
  • Xiaobo Lu, Ruixiang Fei, Li Yang, "Curie temperature of emerging two-dimensional magnetic structures", Phys. Rev. B 100, 205409 (2019).
  • Xiaobo Lu, Xiaoqin Li, Li Yang, "Modulated interlayer exciton properties in a two-dimensional moiré crystal", Phys. Rev. B 100, 155416 (2019).
  • Mu Cao, Ding-Bang Xiong, Li Yang, Shuaishuai Li, Yiqun Xie, Qiang Guo, Zhiqiang Li, Horst Adams, Jiajun Gu, Tongxiang Fan, Xiaohui Zhang, Di Zhang, "Ultrahigh Electrical Conductivity of Graphene Embedded in Metals", Advanced Functional Materials 29, 1806792 (2019).
  • Zhizhan Qiu, Maxim Trushin, Hanyan Fang, Ivan Verzhbitskiy, Shiyuan Gao, Evan Laksono, Ming Yang, Pin Lyu, Jing Li, Jie Su, Mykola Telychko, Kenji Watanabe, Takashi Taniguchi, Jishan Wu, AH Castro Neto, Li Yang, Goki Eda, Shaffique Adam, Jiong Lu, "Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor", Science Advances 7, eaaw2347 (2019).
  • Lingling Ren, Qian Liu, Pengxiang Xu, Zhicheng Zhong, Li Yang, Zhe Yuan, and Ke Xia, "Noncollinearity-modulated Electronic Properties of Monolayer CrI3", Phys. Rev. Applied 11, 054042 (2019).
  • Zhipeng Li, Tianmeng Wang, Chenhao Jin, Zhengguang Lu, Zhen Lian, Yuze Meng, Mark Blei, Shiyuan Gao, Takashi Taniguchi, Kenji Watanabe, Tianhui Ren, Sefaattin Tongay, Li Yang, Dmitry Smirnov, Ting Cao, and Sufei Shi, "Emerging Photoluminescence from the Dark-Exciton Phonon Replica in Monolayer WSe2", Nature Comm. 10, 2469 (2019).
  • Fengnian Xia, Han Wang, James C.M. Hwang, A.H. Castro Neto, and Li Yang, "Black phosphorus and its isoelectronic materials", Nature Phys. Rev. 1, 306 (2019).
  • Kha Tran, Galan Moody, Fengcheng Wu, Xiaobo Lu, Junho Choi, Kyounghwan Kim, Amritesh Rai, Daniel A. Sanchez, Jiamin Quan, Akshay Singh, Jacob Embley, André Zepeda, Marshall Campbell, Travis Autry, Takashi Taniguchi, Kenji Watanabe, Nanshu Lu, Sanjay K. Banerjee, Kevin L. Silverman, Suenne Kim, Emanuel Tutuc, Li Yang, Allan H. MacDonald, and Xiaoqin Li, "Evidence of moiré excitons in van der Waals heterostructures", Nature 567, 71 (2019).
2018
  • Jahyun Koo, Li Yang, and Hoonkyung Lee, "Off-Plane Dielectric Screening of Few-Layer Graphdiyne and Its Family", ACS Appl. Mater. Interfaces 11, 2571 (2018).
  • Shiyuan Gao and Li Yang, "Edge-insensitive magnetism and half metallicity in graphene nanoribbons", J. Phys: Cond. Matt. 30, 48LT01 (2018).
  • Pallavi Malavi, Jing Song, Wenli Bi, Alexander Regnat, Linghan Zhu, Andreas Bauer, Anatoliy Senyshyn, Li Yang, Christian Pfleiderer, and James S. Schilling, "High-pressure investigations on the semi-Heusler compound CuMnSb", Phys. Rev. B 98, 054431 (2018).
  • Yuanyuan Pan, Shiyuan Gao, Li Yang, and Jing Lu, "Dependence of excited-state properties of tellurium on dimensionality: From bulk to two dimensions to one dimensions", Phys. Rev. B 98, 085135 (2018).
  • Galan Moody, Kha Tran, Xiaobo Lu, Travis Autry, James M. Fraser, Richard P. Mirin, Li Yang, Xiaoqin Li, and Kevin L. Silverman, "Microsecond Valley Lifetime of Defect-Bound Excitons in Monolayer WSe2", Phys. Rev. Lett. 121, 057403 (2018).
  • Jizhang Wang, Teng Yang, Zhidong Zhang, and Li Yang, "Enhanced doping effect on tuning structural phases of monolayer antimony", Appl. Phys. Lett. 112, 213104 (2018).
  • Bo Lei, Yuanyuan Pan, Zehua Hu, Jialin Zhang, Du Xiang, Yue Zheng, Rui Guo, Cheng Han, Lianhui Wang, Jing Lu, Li Yang, and Wei Chen, "Direct Observation of Semiconductor–Metal Phase Transition in Bilayer Tungsten Diselenide Induced by Potassium Surface Functionalization", ACS Nano 12, 2070 (2018).
  • Kyle Seyler, Ding Zhong, Dahlia R. Klein, Shiyuan Gao, Xiaoou Zhang, Bevin Huang, Efrén Navarro-Moratalla, Li Yang, David H. Cobden, Michael A. McGuire, Wang Yao, Di Xiao, Pablo Jarillo-Herrero, Xiaodong Xu, "Ligand-field helical luminescence in a 2D ferromagnetic insulator", Nature Phys. 14, 277 (2018).
2017
  • Wenshen Song, Ruixiang Fei, and Li yang, "Off-plane polarization ordering in metal chalcogen diphosphates from bulk to monolayer", Phys. Rev. B 96, 235420 (2017).
  • Shiyuan Gao, Li Yang, and Catalin Spataru, "Interlayer coupling and gate-tunable excitons in transition metal dichalcogenide heterostructures", Nano Lett. 17, 7809 (2017).
  • Xiaolong Chen, Xiaobo Lu, Bingchen Deng, Ofer Sinai, Yuchuan Shao, Cheng Li, Shaofan Yuan, Vy Tran, Kenji Watanabe, Takashi Taniguchi, Doron Naveh, Li Yang, and Fengnian Xia, "Widely tunable black phosphorus mid-infrared photodetector", Nature Comm. 8, 1672 (2017).
  • Jahyun Koo, Shiyuan Gao, Hoonkyung Lee, and Li Yang, "Vertical dielectric screening of few-layer van der Waals semiconductors", Nanoscale 9, 14540 (2017).
  • Xiaobo Lu and Li Yang, "Stark effect of doped two-dimensional transition metal dichalcogenides", Appl. Phys. Lett. 111, 193104 (2017).
  • Nicholas J. Borys, Edward S. Barnard, Shiyuan Gao, Kaiyuan Yao, Wei Bao, Alexander Buyanin, Yingjie Zhang, Sefaattin Tongay, Changhyun Ko, Joonki Suh, Alexander Weber-Bargioni, Junqiao Wu, Li Yang, and P. James Schuck, “Anomalous Above-Gap Photoexcitations and Optical Signatures of Localized Charge Puddles in Monolayer Molybdenum Disulfide”, ACS Nano 11, 2115 (2017).
  • Wenshen Song and Li Yang, "Quasiparticle Band Gaps and Optical Spectra of Strained Monolayer Transition Metal Dichalcogenides", Phys. Rev. B 96, 235441 (2017).
  • Shiyuan Gao and Li Yang, "Renormalization of the quasiparticle band gap in doped two-dimensional materials from many-body calculations", Phys. Rev. B 96, 155410 (2017).
  • Yuanyuan Pan, Yang Dan, Yangyang Wang, Meng Ye, Han Zhang, Ruge Quhe, Xiuying Zhang, Jingzhen Li, Wanlin Guo, Li Yang, and Jing Lu, “Schottky Barriers in Bilayer Phosphorene Transistors”, ACS Appl. Mater. Interfaces 9, 12694 (2017).
  • Bingchen Deng, Vy Tran, Hao Jiang, Cheng Li, Yujun Xie, Qiushi Guo, Xiaomu Wang, He Tian, Steven Koester, Han Wang, Judy Cha, Qiangfei Xia, Li Yang, and Fengnian Xia, "Efficient Electrical Control of Thin-Film Black Phosphorus Bandgap", Nature Comm. 8 14474 (2017).
2016
  • Ruixiang Fei, Wei Kang, and Li Yang, “Ferroelectricity and Phase Transitions in Monolayer Group-IV Monochalcogenides”, Phys. Rev. Lett. 117, 097601 (2016).
  • Shiyuan Gao, Yufeng Liang, Catalin D. Spataru, and Li Yang, “Dynamical Excitonic Effects in Doped Two-Dimensional Semiconductors”, Nano Lett. 16, 5568 (2016).
  • Hongxia Zhong, Ruge Quhe, Yangyang Wang, Zeyuan Ni, Meng Ye, Zhigang Song, Yuanyuan Pan, Jinbo Yang, Li Yang, Ming Lei, Junjie Shi, and Jing Lu, “Interfacial Properties of Monolayer and Bilayer MoS2 Contacts with Metals: Beyond the Energy Band Calculations”, Sci. Rep. 6, 21786 (2016).
  • Minwoo Park, Hyeonhu Bae, Seunghan Lee, Li Yang, and Hoonkyung Lee, "Wedge energy bands of monolayer black phosphorus: a first-principles study", J. Phys. Condens. Matter, 28, 305301 (2016).
  • Zhengning Gao, Fei Wu, Yoon Myung, Ruixiang Fei, Ravindra Kanjolia, Li Yang, and Parag Banerjee, "Standing and sitting adlayers in atomic layer deposition of ZnO", J. Vac. Sci. Technol. 34, 01A143 (2016).
  • Ryan Soklaski, Vy Tran, Zohar Nussinov, KF Kelton, and Li Yang, "A locally preferred structure characterises all dynamical regimes of a supercooled liquid", Philos. Mag. 96, 1212 (2016).
  • He Tian, Jesse Tice, Ruixiang Fei, Vy Tran, Xiaodong Yan, Li Yang, and Han Wang, “Low-symmetry two-dimensional materials for electronic and photonic applications”, Nano Today 11, 763 (2016).
  • Jie Guan, Wenshen Song, Li Yang, David Tománek, "Strain-controlled fundamental gap and structure of bulk black Phosphorus", Phys. Rev. B 94, 045414 (2016).
2015
  • Yufeng Liang and Li Yang, “Carrier Plasmon Induced Nonlinear Band Gap Renormalization in Two-Dimensional Semiconductors”, Phys. Rev. Lett. 114, 063001 (2015).
  • Xiaomu Wang, Aaron M. Jones, Kyle L. Seyler, Vy Tran, Yichen Jia, Huan Zhao, Han Wang, Li Yang, Xiaodong Xu, and Fengnian Xia “Highly anisotropic and robust excitons in monolayer black phosphorus”, Nat. Nanotechnol. 10, 517 (2015).
  • R Fei, V Tran, and Li Yang, “Topologically Protected Dirac Cones in Compressed Bulk Black Phosphorus”, Phys. Rev. B 91, 195319 (2015).
  • Likai Li, Guo Jun Ye, Vy Tran, Ruixiang Fei, Guorui Chen, Huichao Wang, Jian Wang, Kenji Watanabe, Takashi Taniguchi, Li Yang, Xian Hui Chen, and Yuanbo Zhang, “Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films”, Nat. Nanotechnol. 10, 608 (2015).
  • Jia-An Yan, Mack A Dela Cruz, Salvador Barraza-Lopez, and Li Yang, “Strain-tunable topological quantum phase transition in buckled honeycomb lattices”, Appl. Phys. Lett. 106, 183107 (2015).
  • Hong-Xia Zhong, Shiyuan Gao, Jun-Jie Shi, and Li Yang, “Quasiparticle band gaps, excitonic effects, and anisotropic optical properties of the monolayer distorted 1 T diamond-chain structures ReS2 and ReSe2”, Phys. Rev. B 92, 115438 (2015).
  • Hiral Patel, Lola Brown, Yufeng Liang, Li Yang, Jiwoong Park, and Matt W Graham, “Tunable Optical Excitations in Twisted Bilayer Graphene Form Strongly Bound Excitons”, Nano Lett. 15, 5932 (2015).
  • Yanlong Wang, Chunxiao Cong, Ruixiang Fei, Weihuang Yang, Yu Chen, Bingchen Cao, Li Yang, and Ting Yu, “Remarkable anisotropic phonon response in uniaxially strained few-layer black phosphorus”, Nano Research 8, 3944 (2015).
  • Ruixiang Fei, Wenbin Li, Ju Li, and Li Yang, “Giant piezoelectricity of monolayer group IV monochalcogenides: SnSe, SnS, GeSe, and GeS”, Appl. Phys. Lett. 107, 173104 (2015).
  • Vy Tran, Ruixiang Fei, and Li Yang, “Quasiparticle energies, excitons, and optical spectra of few-layer black phosphorus”, 2D materials 2, 044014 (2015).
  • Huan Zhao, Jiangbin Wu, Hongxia Zhong, Qiushi Guo, Xiaomu Wang, Fengnian Xia, Li Yang, Ping-Heng Tan, and Han Wang, "Interlayer Interactions in Anisotropic Atomically-thin Rhenium Diselenide", Interlayer interactions in anisotropic atomically thin rhenium diselenide”, Nano Research 8, 3651 (2015).
  • Yoon Myung, Fei Wu, Sriya Banerjee, Andreea Stoica, Hongxia Zhong, Seung-Soo Lee, John Fortner, Li Yang, and Parag Banerjee, "Highly conducting, n-type Bi12O15Cl6 nanosheets with superlattice-like structure", Chemistry of Materials 27, 7710 (2015).
2014
  • Robin W. Havener, Yufeng Liang, Lola Brown, Li Yang, Jiwoong Park, "Van Hove Singularities and Excitonic Effects in the Optical conductivity of Twisted Bilayer Graphene", Nano Lett. 14, 3353 (2014).
  • A. K. Gangopadhyay, M. E. Blodgett, M. L. Johnson, J. McKnight, V. Wessels, A. J. Vogt, N. A. Mauro, J. C. Bendert, R. Soklaski, L. Yang, and K. F. Kelton, “Anomalous thermal contraction of the first coordination shell in metallic alloy liquids”, J. Chemical Physics, 140, 044505 (2014).
  • Ryan Soklaski, Yufeng Liang, and Li Yang, "Temperature Effect on Optical Spectra of Monolayer Molybdenum Disulfide", Applied Phys. Lett. 104, 193110 (2014).
  • Yufeng Liang, Ryan Soklaski, Shouting Huang, Matthew W. Graham, Robin Havener, Jiwoong Park, Li Yang, "Strongly Bound Excitons in Gapless Two-Dimensional Structures", Phys. Rev. B 90, 115418 (2014).
  • Vy Tran, Ryan Soklaski, Yufeng Liang, Li Yang, "Layer-Controlled Band Gap and Anisotropic Excitons in Few-Layer Black Phosphorus", Phys. Rev. B (Editor’s Suggestion) 89, 235319 (2014).
  • Ruixiang Fei and Li Yang, "Strain-Engineering the Anisotropic Electrical Conductance of Phosphorene and Few-Layer Black Phosphorus", Nano Lett. 14, 2884 (2014).
  • Vy Tran and Li Yang, “Scaling Laws for the Band Gap and Optical Response of Phosphorene Nanoribbons”, Phys. Rev. B 89, 245407 (2014).
  • Ruixiang Fei, Alireza Faghaninia, Ryan Soklaski, Jia-An Yan, Cynthia Lo, and Li Yang, “Enhanced Thermoelectric Efficiency via Orthogonal Electrical and Thermal Conductances in Phosphorene”, Nano Lett. 14, 2884 (2014).
  • Ruixiang Fei and Li Yang, “Lattice Vibrational Modes and Raman Scattering Spectra of Strained Phosphorene”, Appl. Phys. Lett. 105, 083120 (2014).
2013
  • Shouting Huang, Wei Kang and Li Yang, “Electronic Structure and Quasiparticle Bandgap of Silicene Structures”, Appl. Phys. Lett. 102, 133106 (2013).
  • Ryan Soklaski, Zohar Nussinov, Zachary Markow, K. F. Kelton, and Li Yang, "Connectivity of Icosahedral Network and a Dramatically Growing Static Length Scale in Cu-Zr Binary Metallic Glasses", Phys. Rev. B 87, 184203 (2013).
  • Abolhassan Vaezi, Yufeng Liang, Darryl H. Ngai, Li Yang, and Eun-Ah Kim, "Topological Edge States at a Tilt Boundary in Gated Multilayer Graphene", Phys. Rev. X 3, 021018 (2013).
  • Yufeng Liang, Shouting Huang, Ryan Soklaski, and Li Yang, "Quasiparticle Band-Edge Energy and Band Offsets of Monolayer of Molybdenum and Tungsten Chalcogenides", Appl. Phys. Lett. 103, 042106 (2013).
  • N.A. Mauro, A.J. Vogt, M.L. Johnson, J.C. Bendert, R. Soklaski, Li Yang, K.F. Kelton, "Anomalous Structural Evolution and Liquid Fragility Signatures in Cu–Zr and Cu–Hf Liquids and Glasses", Acta Materialia 61, 7411-7421 (2013).
  • S. Huang, Y. Liang and Li Yang, "Exciton Spectra in Two-Dimensional Graphene Derivatives", Phys. Rev. B 88, 075441 (2013).
2012
  • Yufeng Liang, Shouting Huang and Li Yang, “Many-Electron Effects on Optical Absorption Spectra of Strained Graphene”, J. Mater. Res. (Invited feature article) 27, 403-409 (2012).
  • Yufeng Liang and Li Yang, “Quasiparticle Energy and Optical Excitations of Gated Bilayer Graphene”, Phys. Rev. B. 86, 205423 (2012).
2011
  • Li Yang, “Excitons in Intrinsic and Bilayer Graphene”, Phys. Rev. B. 83, 085405 (2011).
  • Shouting Huang and Li Yang, “Strain Engineering of Band Offsets in Si/Ge Core-shell Nanowires”, Appl. Phys. Lett. 98, 093114 (2011).
  • Li Yang and M.Y. Chou, “Lattice Vibrational Modes and their Frequency Shifts in Semiconductor Nanowires”, Nano Lett. 11 (7), 2618 (2011).
  • Yufeng Liang and Li Yang, “Electronic Structure and Optical Absorption of Fluorographene”, MRS Proceedings 1370, 137 (2011).
  • Li Yang, “Excitonic Effects on Optical Absorption Spectra of Doped Graphene”, Nano Lett. 11 (9), 3844 (2011).
2010
  • Li Yang, “First-principles Study of the Optical Absorption Spectra of Electrically Gated Bilayer Graphene”, Phys. Rev. B 81, 155445 (2010).
2009
  • Caglar Girit, Jannik C. Meyer, C. Kisielowski, Li Yang, Cheol-Hwan Park, M. F. Crommie, Marvin L. Cohen, Steven G. Louie, and A. Zettl, “Graphene at the Edge: Stability and Dynamics”, Science 323, 1705 (2009).
  • Cheol-Hwan Park, Young-Woo Son, Li Yang, Marvin L. Cohen, and Steven G. Louie, “Landau Levels and Quantum Hall Effect in Graphene Superlattices”, Phys. Rev. Lett. 103, 046808 (2009).
  • Li Yang, Jack Deslippe, Cheol-Hwan Park, Marvin L. Cohen and Steven G. Louie, “Excitonic Effects on the Optical Response of Graphene and Bilayer Graphene”, Phys. Rev. Lett. 103, 186802 (2009).
2008
  • Li Yang, Ryza N. Musin, Xiao-Qian Wang, M.Y. Chou, “Quantum Confinement Effect in Si/Ge Core-shell Nanowires: First-principles Calculations”, Phys. Rev. B 77, 195325 (2008).
  • Cheol-Hwan Park, Li Yang, Young-Woo Son, Marvin L. Cohen and Steven G. Louie, “Anisotropic Behaviours of Massless Dirac Fermions in Graphene under Periodic Potentials”, Nature Physics 4, 213 (2008).
  • Cheol-Hwan Park, Li Yang, Young-Woo Son, Marvin L. Cohen and Steven G. Louie, “New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials”, Phys. Rev. Lett. 101, 126804 (2008).
  • Cheol-Hwan Park, Young-Woo Son, Li Yang, Marvin L. Cohen and Steven G. Louie, “Electron Beam Supercollimation in Graphene Superlattices”, Nano Lett. 8 (9), 2920 (2008).
  • Li Yang, Marvin L. Cohen and Steven G. Louie, “Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons”, Phys. Rev. Lett. 101, 186401 (2008).
2007
  • Li Yang, Catalin D. Spataru, Steven G. Louie, and M.Y. Chou, “Enhanced Electron-Hole interaction and Optical Absorption in a Silicon Nanowire”, Phys. Rev. B 75, 201304 (2007).
  • Jia-An Yan, Li Yang, and M. Y. Chou, “Size and Orientation Dependence in the Electronic Properties of Silicon Nanowires”, Phys. Rev. B 76, 115319 (2007).
  • Li Yang, Cheol-Hwan Park, Young-Woo Son, Marvin L. Cohen and Steven G. Louie, “Quasiparticle Energies and Band Gaps in Graphene Nanoribbons”, Phys. Rev. Lett. 99, 186801 (2007).
  • Li Yang, Marvin L. Cohen and Steven G. Louie, “Excitonic Effects in the Optical Spectra of Graphene Nanoribbons”, Nano Lett. 7, 3112 (2007).
2005
  • Xinyuan Zhao, C. M. Wei, L. Yang, and M. Y. Chou, “Zhao et al. Reply”, Phys. Rev. Lett. 94, 219702 (2005).
2004
  • A. Peles, J. A. Alford, Z. Ma, Li Yang, and M. Y. Chou, “First-principles Study of NaAlH4 and Na3AlH6 Complex Hydrides”, Phys. Rev. B 70, 165105 (2004).
  • Xinyuan Zhao, C. M. Wei, L. Yang, and M. Y. Chou, “Quantum Confinement and Electronic Properties of Silicon Nanowires”, Phys. Rev. Lett. 92, 236805 (2004).
2001
  • Gang Hu, Zhigang Zheng, Li Yang, Wei Kang, “Thermodynamic Second Law in Irreversible Processes of Chaotic Few-body Systems”, Phys. Rev. E 64, 045102 (2001).