Multiscale Entropy and Its Implications to Critical Phenomena, Emergent Behaviors, and Information

C. Kittel, Introduction to Solid State Physics, Wiley, New York, 2005 S.W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D, 1976, 13, p 191-197 F. Ross, S.W. Hawking, and G.T. Horowitz, Entropy, Area, and Black Hole Pairs, Phys. Rev. D, 1995, 51, p 4302-4314 C.E. Shannon, A Mathematical Theory of Communication, Bell Syst. Tech. J., 1948, 27, p 623-656 S. Pavoine, S. Ollier, and D. Pontier, Measuring Diversity from Dissimilarities with Rao’s Quadratic Entropy: Are Any Dissimilarities Suitable?, Theor. Popul. Biol., 2005, 67, p 231-239 J. Quijano and H. Lin, Entropy in the Critical Zone: A Comprehensive Review, Entropy, 2014, 16, p 3482-3536 M.A. Busa and R.E.A. van Emmerik, Multiscale Entropy: A Tool for Understanding the Complexity of Postural Control, J. Sport Heal. Sci., 2016, 5, p 44-51 Z.K. Liu, Y. Wang, and S.L. Shang, Thermal Expansion Anomaly Regulated by Entropy, Sci. Rep., 2014, 4, p 7043 K.G. Wilson, The Renormalization Group: Critical Phenomena and the Kondo Problem, Rev. Mod. Phys., 1975, 47, p 773-840 A. Pelissetto and E. Vicari, Critical Phenomena and Renormalization-Group Theory, Phys. Rep.-Rev. Sect. Phys. Lett., 2002, 368, p 549-727 Z.K. Liu and Y. Wang, Computational Thermodynamics of Materials, Cambridge University Press, Cambridge, 2016 M. Hillert, Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis, Cambridge University Press, Cambridge, 2008 J.W. Gibbs, The Collected Works of J. Willard Gibbs: Vol. I, Thermodynamics, Yale University Press, New Haven, 1948 Z.K. Liu, X.Y. Li, and Q.M. Zhang, Maximizing the Number of Coexisting Phases Near Invariant Critical Points for Giant Electrocaloric and Electromechanical Responses in Ferroelectrics, Appl. Phys. Lett., 2012, 101, p 82904 D. Kondepudi and I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, Wiley, New York, 1998 J.W. Gibbs, The Collected Works of J. Willard Gibbs: Vol. II, Statistic Mechanics, Yale University Press, New Haven, 1948 S.M. Ross, A First Course in Probability, Pearson, London, 2012 L.D. Landau and E.M. Lifshitz, Statistical Physics, Pergamon Press Ltd., New York, 1980 M. Asta, R. McCormack, and D. de Fontaine, Theoretical Study of Alloy Stability in the Cd-Mg System, Phys. Rev. B, 1993, 48, p 748 Y. Wang, S.L. Shang, H. Zhang, L.Q. Chen, and Z.K. Liu, Thermodynamic Fluctuations in Magnetic States: Fe3Pt as a Prototype, Philos. Mag. Lett., 2010, 90, p 851-859 H.L. Lukas, S.G. Fries, and B. Sundman, Computational Thermodynamics: The CALPHAD Method, Vol 131, Cambridge University Press, Cambridge, 2007 L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagram, Academic Press Inc., New York, 1970 W. Kohn and L.J. Sham, Self-Consisten Equations Including Exchange and Correlation Effects, Phys. Rev., 1965, 140, p A1133-A1138 G. Kresse, J. Furthmüller. Vienna Ab-initio Simulation Package (VASP). https://www.vasp.at. Accessed 13 Jan 2019 Quantum Espresso. http://www.quantum-espresso.org/. Accessed 13 Jan 2019 The Extreme Science and Engineering Discovery Environment (XSEDE). https://www.xsede.org/. Accessed 13 Jan 2019 National Energy Research Scientific Computing Center (NERSC). http://www.nersc.gov/. Accessed 13 Jan 2019 Materials Project. http://materialsproject.org/. Accessed 13 Jan 2019 OQMD: An Open Quantum Materials Database. http://oqmd.org. Accessed 13 Jan 2019 AFLOW: Automatic Flow for Materials Discovery. http://www.aflowlib.org. Accessed 13 Jan 2019 A. van de Walle and G. Ceder, The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics, Rev. Mod. Phys., 2002, 74, p 11-45 Y. Wang, Z.K. Liu, and L.Q. Chen, Thermodynamic Properties of Al, Ni, NiAl, and Ni3Al from First-Principles Calculations, Acta Mater., 2004, 52, p 2665-2671 S.L. Shang, Y. Wang, D. Kim, and Z.K. Liu, First-Principles Thermodynamics from Phonon and Debye Model: Application to Ni and Ni3Al, Comput. Mater. Sci., 2010, 47, p 1040-1048 X.L. Liu, B.K. Vanleeuwen, S.L. Shang, Y. Du, and Z.K. Liu, On the Scaling Factor in Debye–Grüneisen Model: A Case Study of the Mg-Zn Binary System, Comput. Mater. Sci., 2015, 98, p 34-41 S.L. Shang, Y. Wang, and Z.K. Liu, First-Principles Elastic Constants of α- and θ-Al2O3, Appl. Phys. Lett., 2007, 90, p 101909 S.L. Shang, H. Zhang, Y. Wang, and Z.K. Liu, Temperature-Dependent Elastic Stiffness Constants of Alpha- and Theta-Al2O3 from First-Principles Calculations, J. Phys. Condens. Matter, 2010, 22, p 375403 Y. Wang, J.J. Wang, H. Zhang, V.R. Manga, S.L. Shang, L.Q. Chen, and Z.K. Liu, A First-Principles Approach to Finite Temperature Elastic Constants, J. Phys. Condens. Matter, 2010, 22, p 225404 J.M. Sanchez, Cluster Expansion and the Configurational Energy of Alloys, Phys. Rev. B: Condens. Matter, 1993, 48, p R14013-R14015 A. van de Walle, M. Asta, and G. Ceder, The Alloy Theoretic Automated Toolkit: A User Guide, CALPHAD, 2002, 26, p 539-553 A. Zunger, S.H. Wei, L.G. Ferreira, and J.E. Bernard, Special Quasirandom Structures, Phys. Rev. Lett., 1990, 65, p 353-356 C. Jiang, C. Wolverton, J. Sofo, L.Q. Chen, and Z.K. Liu, First-Principles Study of Binary bcc Alloys Using Special Quasirandom Structures, Phys. Rev. B, 2004, 69, p 214202 A. van de Walle, P. Tiwary, M. de Jong, D.L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.-Q. Chen, and Z.K. Liu, Efficient Stochastic Generation of Special Quasirandom Structures, CALPHAD, 2013, 42, p 13-18 R. Car and M. Parrinello, Unified Approach for Molecular-Dynamics and Density-Functional Theory, Phys. Rev. Lett., 1985, 55, p 2471-2474 H.Z. Fang, Y. Wang, S.L. Shang, and Z.K. Liu, Nature of Ferroelectric-Paraelectric Phase Transition and Origin of Negative Thermal Expansion in PbTiO3, Phys. Rev. B, 2015, 91, p 24104 Z.K. Liu, Ocean of Data: Integrating First-Principles Calculations and CALPHAD Modeling with Machine Learning, J. Phase Equilib. Diffus., 2018, 39, p 635-649 Y. Wang, L.G. Hector, H. Zhang, S.L. Shang, L.Q. Chen, and Z.K. Liu, Thermodynamics of the Ce Gamma-Alpha Transition: Density-Functional Study, Phys. Rev. B, 2008, 78, p 104113 G. Kresse, J. Furthmuller, J. Furthmüller, J. Furthmueller, J. Furthmuller, and J. Furthmüller, Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set, Phys. Rev. B, 1996, 54, p 11169 Y. Wang, L.G. Hector, H. Zhang, S.L. Shang, L.Q. Chen, and Z.K. Liu, A Thermodynamic Framework for a System with Itinerant-Electron Magnetism, J. Phys. Condens. Matter, 2009, 21, p 326003 L. Kouwenhoven and L. Glazman, Revival of the Kondo Effect, Phys. World, 2001, 14, p 33-38 Z.K. Liu, Y. Wang, and S.-L. Shang, Origin of Negative Thermal Expansion Phenomenon in Solids, Scr. Mater., 2011, 66, p 130 Z.K. Liu, S.L. Shang, and Y. Wang, Fundamentals of Thermal Expansion and Thermal Contraction, Materials (Basel), 2017, 10, p 410 S.A. Mey, Reevaluation of the Al-Zn System, Z. Met., 1993, 84, p 451-455 Z.K. Liu, Z.G. Mei, Y. Wang, and S.L. Shang, Nature of Ferroelectric–Paraelectric Transition, Philos. Mag. Lett., 2012, 92, p 399-407 G. Shirane and S. Hoshino, On the Phase Transition in Lead Titanate, J. Phys. Soc. Jpn., 1951, 6, p 265 S.G. Jabarov, D.P. Kozlenko, S.E. Kichanov, A.V. Belushkin, B.N. Savenko, R.Z. Mextieva, and C. Lathe, High Pressure Effect on the Ferroelectric-Paraelectric Transition in PbTiO3, Phys. Solid State, 2011, 53, p 2300-2304 D. Damjanovic, Ferroelectric, Dielectric and Piezoelectric Properties of Ferroelectric Thin Films and Ceramics, Rep. Prog. Phys., 1998, 61, p 1267-1324 J. Chen, X. Xing, C. Sun, P. Hu, R. Yu, X. Wang, and L. Li, Zero Thermal Expansion in PbTiO3-Based Perovskites, J. Am. Chem. Soc., 2008, 130, p 1144-1145 P.-E. Janolin, P. Bouvier, J. Kreisel, P.A. Thomas, I.A. Kornev, L. Bellaiche, W. Crichton, M. Hanfland, and B. Dkhil, High-Pressure PbTiO3: An Investigation by Raman and X-Ray Scattering up to 63 GPa, Phys. Rev. Lett., 2008, 101, p 237601 N. Sicron, B. Ravel, Y. Yacoby, E.A. Stern, F. Dogan, and J.J. Rehr, Nature of the Ferroelectric Phase-Transition in PbTiO3, Phys. Rev. B, 1994, 50, p 13168-13180 K. Sato, T. Miyanaga, S. Ikeda, and D. Diop, XAFS Study of Local Structure Change in Perovskite Titanates, Phys. Scr., 2005, 2005, p 359 W. Cochran and R.A. Cowley, Dielectric Constants and Lattice Vibrations, J. Phys. Chem. Solids, 1962, 23, p 447-450 Y. Wang, J.J. Wang, W.Y. Wang, Z.G. Mei, S.L. Shang, L.Q. Chen, and Z.K. Liu, A Mixed-Space Approach to First-Principles Calculations of Phonon Frequencies for Polar Materials, J. Phys.-Condens. Matter, 2010, 22, p 202201 Y. Wang, S.L. Shang, H. Fang, Z.K. Liu, and L.Q. Chen, First-Principles Calculations of Lattice Dynamics and Thermal Properties of Polar Solids, Comput. Mater., 2016, 2, p 16006 Y. Wang, J.E. Saal, Z.G. Mei, P.P. Wu, J.J. Wang, S.L. Shang, Z.K. Liu, and L.Q. Chen, A First-Principles Scheme to Phonons of High Temperature Phase: No Imaginary Modes for Cubic SrTiO3, Appl. Phys. Lett., 2010, 97, p 162907 M.J. Zhou, Y. Wang, Y. Ji, Z.K. Liu, L.Q. Chen, and C.-W. Nan, First-Principles Lattice Dynamics and Thermodynamic Properties of Pre-Perovskite PbTiO3, Acta Mater, 2019, 171, p 146-153 L. Szilard, Uber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen, Z. Phys., 1929, 53, p 840-856 L. Szilard, On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings, Behav. Sci., 1964, 9, p 301-310 C.E. Shannon, Prediction and Entropy of Printed English, Bell Syst. Tech. J., 1951, 30, p 50-64 L. Brillouin, Physical Entropy and Information. II, J. Appl. Phys., 1951, 22, p 338-343 L. Brillouin, The Negentropy Principle of Information, J. Appl. Phys., 1953, 24, p 1152-1163 L. Brillouin, Information Theory and Its Applications to Fundamental Problems in Physics, Nature, 1959, 183, p 501-502 L. Brillouin, Thermodynamics, Statistics, and Information, Am. J. Phys., 1961, 29, p 318-328 L. Brillouin, Science and Information Theory, Academic Press, New York, 1962 K. Maruyama, F. Nori, and V. Vedral, Colloquium: The Physics of Maxwell’s Demon and Information, Rev. Mod. Phys., 2009, 81, p 1-23 R. Landauer, Irreversibility and Heat Generation in the Computing Process, IBM J. Res. Dev., 1961, 5, p 183-191 R. Landauer, Dissipation and Noise Immunity in Computation and Communication, Nature, 1988, 335, p 779-784 C.H. Bennett, The Thermodynamics of Computation—A Review, Int. J. Theor. Phys., 1982, 21, p 905-940 S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental Demonstration of Information-to-Energy Conversion and Validation of the Generalized Jarzynski Equality, Nat. Phys., 2010, 6, p 988-992 A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, Experimental Verification of Landauer’s Principle Linking Information and Thermodynamics, Nature, 2012, 483, p 187-189 L. Brillouin, Negentropy and Information in Telecommunications, Writing, and Reading, J. Appl. Phys., 1954, 25, p 595-599 U. Seifert, Stochastic Thermodynamics, Fluctuation Theorems and Molecular Machines, Rep. Prog. Phys., 2012, 75, p 126001 P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Quantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions, Phys. Rev. X, 2017, 7, p 021003 E. Pop, Energy Dissipation and Transport in Nanoscale Devices, Nano Res, 2010, 3, p 147-169 S. Vinjanampathy and J. Anders, Quantum Thermodynamics, Contemp. Phys., 2016, 57, p 545-579 S.E. Jørgensen, A New Ecology: Systems Perspective, Elsevier, Amsterdam, 2007 B. Ravel, N. Slcron, Y. Yacoby, E.A. Stern, F. Dogan, and J.J. Rehr, Order-Disorder Behavior in the Phase Transition of PbTiO3, Ferroelectrics, 1995, 164, p 265-277