Statistical Mechanics (and Condensed Matter)

01 Apr 2003 09:01

The first mathematical, natural science of emergent properties. (I hedge this way, because one could argue that economics and evolutionary theory are both, also, concerned with emergent properties --- efficient allocation, and adaptation and speciation, respectively, and they preceeded statistical mechanics.) The heart of the subject is figuring out what happens when vast numbers of particles bounce around and into each other, all obeying the laws of mechanics (classical or quantum as the case may be).

Things I Want to Understand Better: Phase transitions and critical phenoma; the renormalization group; field-theory methods; what happens far from equilibrium (more specifically, are there action principles or the like that govern probability distributions of trajectories, the way thermodynamic potentials govern equilibrium configurations); "soft" condensed matter; biological applications; amorphous materials and glasses; connections between spin glasses and biology (e.g., perceptrons); technical, conceptual and historical issues in the foundations of statistical mechanics.

Recommended:

<rant> If a non-scientist wants to learn about some large and important part of science, say planetary astronomy or genetics, there are usually a handful of reliable, uncontroversial, well-written, non-technical books about it to be found in the stores and libraries, which will convey at least something of the field's history, problems, results and methods. By this point there must be dozens of good popular books written on evolution, particle physics, cosmology, relativity and quantum mechanics, notwithstanding that the last two are about as abstract and abstruse as science gets. There are even excellent popularizations of mathematics, in a continuous tradition from E. T. Bell (if not before). Writing popularizations is an accepted and even encouraged activity for eminent scientists, and has been since Galileo's Starry Messanger. --- Popularizations are also important in the recruitment and education of scientists, but the only one I know of who's written on this is John Maynard Smith, in Did Darwin Get It Right?

A few months ago, when I was trying to explain some parts of my research to my father, I realized I was assuming he knew what statistical mechanics was, and something about how it worked, when in fact he did not. My first thought was to pass on some popular work about statistical mechanics (it's only fair; he did it to me constantly when I was younger). A great many thoughts later I realized I could not think of a single one which didn't stake out some very peculiar philosophical position, or did more than just blab about the second law, never mind something as good as Einstein for Beginners or The First Three Minutes or Does God Play Dice? Granted that relativity and particles and chaos are sexy, and statistical mechanics is not, it's peculiar that there's nothing. Stat. mech. is, after all, one of the essential theories of current physics, actually used by chemists and biologists and materials scientists, etc., the part of physics most directly applicable to daily life (you could illustrate the core of it with a coffee cup, and the whole with a kitchen), and bound up with deep puzzles about why time goes the way it does. This cries out for a remedy.

The undergraduate textbooks on statistical mechanics, like those on most part of physics, are by and large vile. Kittel and Kroemer's Thermal Physics is however decent; if you want a quick-and-dirty guide, and can put up with bad typesetting, try M. G. Bowler's Lectures on Statistical Mechanics. There is nothing analogous to Griffiths's books on electromagnetism, quantum mechanics and particle physics, and if he's got time on his hands...

Chandler's Introduction to Modern Statistical Mechanics is good, as is Landau and Lifshitz's Statistical Physics; the latter is far more comprehensive, but the former is much newer, and easier to learn from. Huang's Statistical Mechanics, one of the other standard texts, is a pedagogic horror.

Having finished this venting of spleen, we turn to the usual list. </rant>

Vinay Ambegaokar, Reasoning about Luck: Probability and Its Uses in Physics [This is intended as a substitute for the usual sort of physics-for-people-who-have-to-fill-a-distribution-requirement course, and I think well enough of it that I'd be willing to teach it, while wild horses couldn't get me to do the standard physics for poets, but it's not really what I'm looking for.]
David Ruelle, Chance and Chaos [Parts of this approach what I was raving for above, but still doesn't quite hack it, since it doesn't cover enough.]
Hans Christian von Baeyer, Maxwell's Demon: Why Warmth Disperses and Time Passes [Again, almost makes it]

Philip W. Anderson, Basic Notions of Condensed Matter Physics
Beck and Schlögl, Thermodynamics of Chaotic Systems [See notice under non-linear dynamics]
Britney Spears's Guide to Semiconductor Physics
Chaikin and Lubensky, Principles of Condensed Matter
Richard S. Ellis, Entropy, Large Deviations and Statistical Mechanics
K. H. Fischer and J. A. Hertz, Spin Glasses
Dieter Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions [An excellent book which looks horrible. Bless Donald Knuth for delivering us from type-writen equations!]
D. H. E. Gross, "Microscopic statistical basis of classical Thermodynamics of finite systems", cond-mat/0505242
Meir Hemmo and Orly Shenker, "Quantum Decoherence and the Approach to Equilibrium", Philosophy of Science 70 (2003): 330--358
Chris Hillman, Entropy on the World Wide Web
Mark Kac, Probability in Physical Sciences and Related Topics
Joel L. Lebowitz, "Statistical mechanics: A selective Review of Two Central Issues", Reviews of Modern Physics 71 (1999): S346--S357, math-ph/0010018 [Abstract: "I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time-asymmetric evolution of macroscopic systems towards equilibrium and of first-order phase transitions in equilibrium. These phenomena are emergent collective properties not discernible in the behavior of individual atoms. They are given precise and elegant mathematical formulations when the ratio between macroscopic and microscopic scales becomes very large."]
L. D. Landau and E. M. Lifshitz, Statistical Physics [What I was raised on. To be completely honest, it's been about a decade since I read it, and more since it was my constant companion, and I am a little afraid to re-read it, the same way one is sometimes afraid to re-read favorite novels from long ago, lest they have become worse in the meanwhile...]
David Selmeczi, Simon F. Tolic-Norrelykke, Erik Schaeffer, Peter H. Hagedorn, Stephan Mosler, Kirstine Berg-Sorensen, Niels B. Larsen and Henrik Flyvbjerg, "Brownian Motion after Einstein: Some new applications and new experiments", physics/0603142
James Sethna, "Order Parameters, Broken Symmetry, and Topology", pp. 243--265 in Lynn Nadel and Daniel L. Stein (eds.), 1990 Lectures in Complex Systems
Geoffrey Sewell, Quantum Mechanics and Its Emergent Macrophysics
Julia Yeomans, The Statistical Mechanics of Phase Transitions
Richard Zallen, The Physics of Amorphous Solids

CRS and Cristopher Moore, "What Is a Macrotate?" cond-mat/0303625

Stephen Brush
- Statistical Physics and the Atomic Theory of Matter
- The Kind of Motion We Call Heat
M. E. Cates, "Soft Condensed Matter", cond-mat/0411650 ["I described the evolution of soft matter physics as a discipline during the 20th century"]
Cyril Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena
Albert Einstein, Investigations on the Theory of Brownian Motion
Martin Niss, "History of the Lenz-Ising Model, 1920--1950: From Ferromagnetic to Cooperative Phenomena", Archive for History of Exact Sciences 59 (2005): 267--318 [Journal link. From the abstract: "I chart the considerable changes in the status and conception of the Lenz-Ising model from 1920 to 1950 in terms of three phases: In the early 1920s, Lenz and Ising introduced the model in the field of ferromagnetism. Based on an exact derivation, Ising concluded that it is incapable of displaying ferromagnetic behavior, a result he erroneously extended to three dimensions. In the next phase, Lenz and Ising's contemporaries rejected the model as a representation of ferromagnetic materials because of its conflict with the new quantum mechanics. In the third phase, from the early 1930s to the early 1940s, the model was revived as a model of cooperative phenomena. ... [I] focus on the development of the model in its capacity as a model. ... A major theme of my study is that even though the Lenz-Ising model is not fully realistic, it is more useful than more realistic models because of its mathematical tractability. I argue that this point of view, important for the modern conception of the model, is novel and that its emergence, while perhaps not a consequence of its study, is coincident with the third phase of its development." Those of us who work with grossly unrealistic but tractable models of complex systems should pay heed...]
Johanna Levelt Sengers, How Fluids Unmix: Discoveries by the School of Van der Waals and Kamerlingh Onnes [Blurb]
D. ter Haar, The Scientific Contributions of H. A. Kramers [blurb]

Greg Anderson, Thermodynamics of Natural Systems
Roger Balian
From Microphysics to Macrophysics: Methods and Applications of Statistical Physics
RB and Jean-Paul Blaizot, "Stars and Statistical Physics: A Teaching Experience," cond-mat/9909291 [I plan to steal from this wholesale if I teach stat. mech.]
Giovanni Gallavotti, "Equilibrium Statistical Mechanics", cond-mat/0504790 [56 pp. introductory review]
Martin and Inge F. Goldstein, The Refrigerator and the Universe
Josef Honerkamp, Statistical Physics: An Advanced Approach with Applications
Charles Kittel, Elementary Statistical Physics [1958 textbook now republished in Dover paperback; looks good and cheap; I learned a lot from Kittel and Kromer's textbook as an undergraduate]
R. A. Minlos, Introduction to Mathematical Statistical Physics [Blurb]
James Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity [Blurb]

Ambjorn, Durhuss and Jonsson, Quantum Geometry [field-theory methods for Brownian motion and higher-dimensional random surfaces]
Roger Balian
- "Incomplete Descriptions and Relevant Entropies," cond-mat/9907015
- "Information in statistical physics", cond-mat/0501322
Francois Bardou et al., Levy Statistics and Laser Cooling: How Rare Events Bring Atoms to Rest
Jean-Louis Barrat and Jean-Pierre Hansen, Basic Concepts for Simple and Complex Liquids
Rodney J. Baxter, Exactly Solved Models in Statistical Mechanics [Blurb]
Golan Bel and Eli Barkai, "A Random Walk to a Non-Ergodic Equilibrium Concept", cond-mat/0506338 [I've only read the abstract, but it puzzles me. I'd be very interested if we could have a good notion of equilibrium which didn't depend on ergodicity, but in the model they're consdering, they can evidently say things like "in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point, approaches U or W shaped distributions related to the arcsin law", and I'm not sure how such limits are meaningful without some kind of ergodic property. But I should just read the paper.]
Federico Bonetto and Joel Lebowitz, "Thermodynamic entropy production fluctuation in a two dimensional shear flow model," nlin.CD/0103044
Anton Bovier, Statistical Mechanics of Disordered Systems [Blurb]
Anton Bovier, Michael Eckhoff, Veronique Gayrard and Markus Klein, "Metastability and Small Eigenvalues in Markov Chains," cond-mat/0007343
Todd A. Brun and James B. Hartle, "Entropy of Classical Histories," Physical Review E 59 (1999): 6370--6380
Lapo Casetti, Marco Pettini, E. G. D. Cohen, "Geometric Approach to Hamiltonian Dynamics and Statistical Mechanics," cond-mat/9912092
Tommaso Castellani and Andrea Cavagna, "Spin-Glass Theory for Pedestrians", cond-mat/0505032
Emilio De Santis and Carlo Marinelli, "Stochastic games with infinitely many interacting agents", math.PR/0505608 [Sounds very cool: "We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove ``fixation'', i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zero-temperature Glauber dynamics on random graphs of possibly infinite volume."]
Deepak Dhar, "Pico-canonical ensembles: A theoretical description of metastable states," cond-mat/0205011
Enrico Di Cera, Thermodynamic Theory of Site-Specific Binding Processes in Biological Macromolecules
E. Dinaburg, C. Maes, S. Pirogov, F. Redig and A. Rybko, "The Potts model built on sand", cond-mt/0312363
Viktor Dotsenko, Introduction to the Replica Theory of Disordered Statistical Systems
Sam F. Edwards and Moshe Schwartz
- "Lagrangian Statistical Mechanics applied to Non-linear Stochastic Field Equations," cond-mat/0012044
- "Statistical Mechanics in Collective Coordinates," cond-mat/0204178
Denis J. Evans, E. G. D. Cohen, Debra J. Searles and Federico Bonetto, "Note on the Kaplan-Yorke Dimension and Linear Transport Coefficients," cond-mat/9911455
David Ford and Steven Huntsman, "Descriptive Thermodynamics", cond-mat/0510030
A. Gabrielli, B. Jancovici, M. Joyce, J. L. Lebowitz, L. Pietronero and F. Sylos Labini, "Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models," astro-ph/0210033 [I need a cosmology notebook]
A. Gabrielli, F. Sylos Labini, M. Joyce and L. Pietronero, Statistical Physics for Cosmic Structures [Extremely positive review in J. Stat. Phys.]
Cristian Giardina', Jorge Kurchan, Luca Peliti, "Direct evaluation of large-deviation functions", cond-mat/0511248 ["We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical properties of a modified dynamics, and since they no longer involve rare events, can be evaluated efficiently and over a wider ranges of values."]
G. Gregoire and H. Chate, "Onset of collective and cohesive motion", cond-mat/0401208
J. Woods Halley, Statistical Mechanics: From First Principles to Macroscopic Phenomena [blurb. Sounds nice.]
Andreas Hanke and Ralf Metzler, "Towards the molecular workshop: entropy-driven designer molecules, entropy activation, and nanomechanical devices," cond-mat/0203539
Horsthemke, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology
Stephen Hyde, Sten Andersson, Kare Larsson, Zoltan Blum, Tomas Landh, Sven Lidin and Barry Ninham, The Language of Shape: The Role of Curvature in Condensed Matter --- Physics, Chemistry, and Biology
Claude Itzykson and Jean-Michel Drouffe, Statistical Field Theory (2 vols.)
Henrik Jeldtoft Jensen, Elsa Arcaute, "Complexity, Collective Effects and Modelling of Ecosystems: formation, function and stability", arxiv:0709.2015 [" We describe examples where combining statistical mechanics and ecology has led to improved ecological modelling and, at the same time, broadened the scope of statistical mechanics."]
Richard A. L. Jones, Soft Condensed Matter
Wouter Kager and Bernard Nienhuis, "A Guide to Stochastic Loewner Evolution and Its Applications", math-ph/0312056
T. R. Kirkpatrick, D. Belitz, and J. V. Sengers, "Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior," cond-mat/0110603
Tsampikos Kottos and Doron Cohen, "Quantum Irreversibility of Energy Spreading," cond-mat/0201148
Werner Krauth, Statistical Mechanics: Algorithms and Computations
Karsten Kruse, Jean-Francois Joanny, Frank Julicher, Jacques Prost and Ken Sekimoto, "Generic theory of active polar gels: A paradigm for cytoskeletal dynamics", physics/0406058
Stephan Lawi, "A characterization of Markov processes enjoying the time-inversion property", math.PR/0506013
Elliott H. Lieb, "Quantum Mechanics, the Stability of Matter and Quantum Electrodynamics", math-ph/0401004
D. Lynden-Bell and R. M. Lynden-Bell, "Relaxation to a Perpetually Pulsating Equilibrium", cond-mat/0401093 = Journal of Statistical Physics 117 (2004): 199--209 [A profoundly weird-looking result]
Ferdinando Mancini, "New perspectives on the Ising model", cond-mat/0506117 [Who'd've thought there was anything new to say about the Ising model? But the abstract actually sounds neat: "The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which holds for any dimensionality of the system. The Hamiltonian of the model is solved in terms of a complete finite set of eigenoperators and eigenvalues. The Green's function and the correlation functions of the fermionic model are exactly known and are expressed in terms of a finite small number of parameters that have to be self-consistently determined. By using the equation of the motion method, we derive a set of equations which connect different spin correlation functions. The scheme that emerges is that it is possible to describe the Ising model from a unified point of view where all the properties are connected to a small number of local parameters, and where the critical behavior is controlled by the energy scales fixed by the eigenvalues of the Hamiltonian. By using algebra and symmetry considerations, we calculate the self-consistent parameters for the one-dimensional case. All the properties of the system are calculated and obviously agree with the exact results reported in the literature."]
Carl McBride, "Computers and Liquid State Statistical Mechanics", cond-mat/0610771
Robert K. Niven, "Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics", cond-mat/0412460 ["The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities..."]
Alessandro Pelizzola, "Cluster variation method in statistical physics and probabilistic graphical models", Journal of Physics A: Mathematical and General 38 (2005): R309--R339 = cond-mat/0508216
Sebastian Risau-Gusman, Alexandre S. Martinez and Osame Kinouchi, "Escaping from cycles through a glass transition," cond-mat/0301147
Hans Henrik Rugh, "A Micro-Thermodynamic Formalism," nlin.CD/0201062
Michel Talagrand, Mean Field Models for Spin Glasses: A First Course [110 pp. MS.; thanks to Alessandro Rinaldo for sharing his copy with me]
Y. Vallis, T. Qu, M. Micoulaut, F. Chaimbault and P. Boolchand, "Direct evidence of rigidity loss and self-organisation in silicate glasses", cond-mat/0406509
David Wales, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses [Blurb]
Paolo Zanardi, Paolo Giorda, and Marco Cozzini, "Information-Theoretic Differential Geometry of Quantum Phase Transitions", Physical Review Letters 99 (2007): 100603