Conclusion: the Impact of Statistical Physics

Total Page:16

File Type:pdf, Size:1020Kb

Conclusion: the Impact of Statistical Physics Conclusion: The Impact of Statistical Physics Applications of Statistical Physics The different examples which we have treated in the present book have shown the role played by statistical mechanics in other branches of physics: as a theory of matter in its various forms it serves as a bridge between macroscopic physics, which is more descriptive and experimental, and microscopic physics, which aims at finding the principles on which our understanding of Nature is based. This bridge can be crossed fruitfully in both directions, to explain or predict macroscopic properties from our knowledge of microphysics, and inversely to consolidate the microscopic principles by exploring their more or less distant macroscopic consequences which may be checked experimentally. The use of statistical methods for deductive purposes becomes unavoidable as soon as the systems or the effects studied are no longer elementary. Statistical physics is a tool of common use in the other natural sciences. Astrophysics resorts to it for describing the various forms of matter existing in the Universe where densities are either too high or too low, and tempera­ tures too high, to enable us to carry out the appropriate laboratory studies. Chemical kinetics as well as chemical equilibria depend in an essential way on it. We have also seen that this makes it possible to calculate the mechan­ ical properties of fluids or of solids; these properties are postulated in the mechanics of continuous media. Even biophysics has recourse to it when it treats general properties or poorly organized systems. If we turn to the domain of practical applications it is clear that the technology of materials, a science aiming to develop substances which have definite mechanical (metallurgy, plastics, lubricants), chemical (corrosion), thermal (conduction or insulation), electrical (resistance, superconductivity), or optical (display by liquid crystals) properties, has a great interest in statis­ tical physics. For instance, ferromagnetism, a phenomenon which is of great importance as it has enabled the development of electrical engineering (alter­ nators, transformers, motors), is the result of an order-disorder phase transi­ tion; we have sketched its theory in Chap.9. Here, observations and practical applications preceded understanding. However, we have shown in Chap.11 how the theory of another kind of substances, the semiconductors, has led to the construction of devices such as diodes or transistors and everybody knows their innumerable applications (micro-electronics, computers, energetics). 572 Conclusion: The Impact of Statistical Physics Through thermodynamics, which has become its extension, but also di­ rectly, statistical physics contributes to the development of various energy techniques, whether the extraction, transformation, transport, storage, sav­ ing, or efficient use of thermal, electrical, radiative, chemical, mechanical, or nuclear energy. In passing we have mentioned some applications to the quest for new energy sources, such as fusion or solar energy. Methods and Concepts of Statistical Physics Statistical physics has also played a major role in the realm of ideas. Like rela­ tivity and quantum mechanics, and maybe even more deeply, it has changed our world picture through its philosophical impact and its epistemological implications. As we have seen several times it has accustomed us, even out­ side the framework of quantum theory, to incorporate in science a partially subjective, or at least a relative, aspect inherent in the probability concept. We see now scientific progress as a devolution of more and more probable, more and more faithful, images of reality, but the belief in an absolute sci­ entific Truth, which was so widespread amongst scientists and philosophers in the nineteenth century, can hardly be found nowadays: more or less great likelihood, yes, but no final certainty. Also noteworthy are the contributions of statistical physics to the devel­ opment of methods and concepts. It was one of the first disciplines where the statistical method, that is the art of making predictions when one has little knowledge, was worked out. A macroscopic substance is a typical example of a system which is too complicated to be described in all detail. The proper­ ties in which we are interested concern only a few degrees of freedom, or are average effects; the statistical treatment allows us to discard those aspects that are too complicated, not well known, or of no interest. This fruitful ap­ proach is met with in all applications of statistics. We have also illustrated another remarkable possibility opened up by statistics, to wit, the possibil­ ity to m^ake nearly certain predictions even though the system studied has a random nature, provided it is large. Another method, examples of which can be found in Chaps.7 or 15, dealing with transport, and 13, dealing with Kirchhoff's laws, consists in making up a detailed balance of exchanges which can take place between one part of the system and another. Conservation laws, such as those for energy, momentum, or particle numbers, play an important role in establishing this balance and this enables us to reduce the problem. These ideas can be transposed to economic sciences. We also saw in Chap.14 how fruitful is the systematic exploitation of symmetry and invariance properties. Statistical physics is a field where the use of models is a nearly perma­ nent feature. The ideal method, which would consist of starting from a known Hamiltonian to use a Boltzmann-Gibbs distribution for deriving the proper- Methods and Concepts of Statistical Physics 573 ties of a system, often turns out to be intractable. Therefore, as we did on many occasions in this book, one does not start from first principles, but one uses a model, that is, a simple, idealized structure, which is meant to depict consistently a more complicated reality. It even happens that one introduces contradictory models to describe different aspects of the same system. One knows that the social sciences, such as economics and sociology, make great use of models. Statistical physics can help us understand the significance of their use. In fact, in fields where theory is not so well developed, one is prepared to justify a model by its operational fertility and by more or less intuitive similarity arguments. In statistical physics, we can go further, as we saw at the end of Chap.l, by constructing a series of more and more refined models which are based partly upon more and more precise experiments, and partly upon known "first principles" from which approximations enable us to construct models. These nested models are successive steps in the capture of Nature. Several concepts introduced in statistical physics have already passed into everyday usage. It suffices to mention energy, its transformations and the consequences of its conservation: the limitation of our energy resources, on the one hand, and the inevitability of "thermal pollution" if one uses energy, on the other hand, have become commonplace. We have studied the relations between the concepts of entropy, informa­ tion, and disorder. Energy degradation, and irreversibility, are manifestations of the general tendency towards the loss of order. We also saw that when we increase our knowledge about a system, we put order into it. These kinds of considerations by and large go beyond the framework of physics. Especially, information theory, the birth of which was partly due to statistical physics, enables us to improve the efiiciency of transmission methods by using a suit­ able treatment of messages which avoids their being tangled up by noise. Prom this point of view, a sizeable part of biology appears as the study of mechanisms through which living organisms create order by using the infor­ mation contained in their genetic code. Is even intellectual activity nothing but a struggle against chaos? A set of remarkable effects, which may also be found outside statistical physics, is connected with the establishing of order in a system. We have been able to appreciate the diversity of the forms that order can take, from mag­ netism to the superfluidity of helium. The huge variety of crystal structures provide us with a spectacular example of this wealth of types of ordering. We saw also (§§ 11.1.2 and 12.2.3) that different forms of order may compete and that depending on the situation, one or other of them dominates. The a pri­ ori most surprising phenomenon is the sudden appearance of order: we have encountered several examples of phase transitions where a qualitative change is suddenly produced when the temperature is gradually lowered. Statisti­ cal physics enables us to understand the origin of such discontinuities which occur only thanks to the large size of the systems studied. 574 Conclusion: The Impact of Statistical Physics Finally, statistical physics clearly illustrates the concept of hierarchical structures, which is fashionable in human sciences. Depending on the scale in which we are interested, the laws of physics differ: a substance is on the microscopic scale a set of electrons and nuclei interacting through Coulomb forces; on the macroscopic scale, it is a gas or a solid with an order which we could not expect from the microscopic laws. However, the physicist believes in the existence of universal fundamental laws, or at least in the possibility of gradually unifying the various pieces of information available at a given time. Statistical physics helps us to resolve this contradiction between the unity of Nature and the change of her laws depending on the scale, by enabling us to derive a large number of macroscopic laws from the underlying microscopic laws. On the level of principles, the latter, which are simpler, appear to be more fundamental. On the practical level, the fact that this derivation is pos­ sible in relatively simple cases, all the same, does not transform macroscopic physics or chemistry into disciplines with the logical and consistent structure of mathematics: the constituent elements of reality are simple, but combining them leads to enormously rich complex phenomena.
Recommended publications
  • Arxiv:1509.06955V1 [Physics.Optics]
    Statistical mechanics models for multimode lasers and random lasers F. Antenucci 1,2, A. Crisanti2,3, M. Ib´a˜nez Berganza2,4, A. Marruzzo1,2, L. Leuzzi1,2∗ 1 NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Lab, Rome, Piazzale A. Moro 2, I-00185, Roma, Italy 2 Dipartimento di Fisica, Universit`adi Roma “Sapienza,” Piazzale A. Moro 2, I-00185, Roma, Italy 3 ISC-CNR, UOS Sapienza, Piazzale A. Moro 2, I-00185, Roma, Italy 4 INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replica method. For high degrees of disorder and nonlinearity, a glassy behavior is expected at the lasing threshold, providing a suggestive link between glasses and photonics. We describe in details the results for the general Hamiltonian model in mean field approximation and mention an available test for replica symmetry breaking from intensity spectra measurements. Finally, we summary some perspectives still opened for such approaches. The idea that the lasing threshold can be understood as a proper thermodynamic transition goes back since the early development of laser theory and non-linear optics in the 1970s, in particular in connection with modulation instability (see, e.g.,1 and the review2).
    [Show full text]
  • Research Statement Statistical Physics Methods and Large Scale
    Research Statement Maxim Shkarayev Statistical physics methods and large scale computations In recent years, the methods of statistical physics have found applications in many seemingly un- related areas, such as in information technology and bio-physics. The core of my recent research is largely based on developing and utilizing these methods in the novel areas of applied mathemat- ics: evaluation of error statistics in communication systems and dynamics of neuronal networks. During the coarse of my work I have shown that the distribution of the error rates in the fiber op- tical communication systems has broad tails; I have also shown that the architectural connectivity of the neuronal networks implies the functional connectivity of the afore mentioned networks. In my work I have successfully developed and applied methods based on optimal fluctuation theory, mean-field theory, asymptotic analysis. These methods can be used in investigations of related areas. Optical Communication Systems Error Rate Statistics in Fiber Optical Communication Links. During my studies in the Ap- plied Mathematics Program at the University of Arizona, my research was focused on the analyti- cal, numerical and experimental study of the statistics of rare events. In many cases the event that has the greatest impact is of extremely small likelihood. For example, large magnitude earthquakes are not at all frequent, yet their impact is so dramatic that understanding the likelihood of their oc- currence is of great practical value. Studying the statistical properties of rare events is nontrivial because these events are infrequent and there is rarely sufficient time to observe the event enough times to assess any information about its statistics.
    [Show full text]
  • Statistical Physics II
    Statistical Physics II. Janos Polonyi Strasbourg University (Dated: May 9, 2019) Contents I. Equilibrium ensembles 3 A. Closed systems 3 B. Randomness and macroscopic physics 5 C. Heat exchange 6 D. Information 8 E. Correlations and informations 11 F. Maximal entropy principle 12 G. Ensembles 13 H. Second law of thermodynamics 16 I. What is entropy after all? 18 J. Grand canonical ensemble, quantum case 19 K. Noninteracting particles 20 II. Perturbation expansion 22 A. Exchange correlations for free particles 23 B. Interacting classical systems 27 C. Interacting quantum systems 29 III. Phase transitions 30 A. Thermodynamics 32 B. Spontaneous symmetry breaking and order parameter 33 C. Singularities of the partition function 35 IV. Spin models on lattice 37 A. Effective theories 37 B. Spin models 38 C. Ising model in one dimension 39 D. High temperature expansion for the Ising model 41 E. Ordered phase in the Ising model in two dimension dimensions 41 V. Critical phenomena 43 A. Correlation length 44 B. Scaling laws 45 C. Scaling laws from the correlation function 47 D. Landau-Ginzburg double expansion 49 E. Mean field solution 50 F. Fluctuations and the critical point 55 VI. Bose systems 56 A. Noninteracting bosons 56 B. Phases of Helium 58 C. He II 59 D. Energy damping in super-fluid 60 E. Vortices 61 VII. Nonequillibrium processes 62 A. Stochastic processes 62 B. Markov process 63 2 C. Markov chain 64 D. Master equation 65 E. Equilibrium 66 VIII. Brownian motion 66 A. Diffusion equation 66 B. Fokker-Planck equation 68 IX. Linear response 72 A.
    [Show full text]
  • Chapter 7 Equilibrium Statistical Physics
    Chapter 7 Equilibrium statistical physics 7.1 Introduction The movement and the internal excitation states of atoms and molecules constitute the microscopic basis of thermodynamics. It is the task of statistical physics to connect the microscopic theory, viz the classical and quantum mechanical equations of motion, with the macroscopic laws of thermodynamics. Thermodynamic limit The number of particles in a macroscopic system is of the order of the Avogadro constantN 6 10 23 and hence huge. An exact solution of 1023 coupled a ∼ · equations of motion will hence not be possible, neither analytically,∗ nor numerically.† In statistical physics we will be dealing therefore with probability distribution functions describing averaged quantities and theirfluctuations. Intensive quantities like the free energy per volume,F/V will then have a well defined thermodynamic limit F lim . (7.1) N →∞ V The existence of a well defined thermodynamic limit (7.1) rests on the law of large num- bers, which implies thatfluctuations scale as 1/ √N. The statistics of intensive quantities reduce hence to an evaluation of their mean forN . →∞ Branches of statistical physics. We can distinguish the following branches of statistical physics. Classical statistical physics. The microscopic equations of motion of the particles are • given by classical mechanics. Classical statistical physics is incomplete in the sense that additional assumptions are needed for a rigorous derivation of thermodynamics. Quantum statistical physics. The microscopic equations of quantum mechanics pro- • vide the complete and self-contained basis of statistical physics once the statistical ensemble is defined. ∗ In classical mechanics one can solve only the two-body problem analytically, the Kepler problem, but not the problem of three or more interacting celestial bodies.
    [Show full text]
  • Quantum Statistical Physics: a New Approach
    QUANTUM STATISTICAL PHYSICS: A NEW APPROACH U. F. Edgal*,†,‡ and D. L. Huber‡ School of Technology, North Carolina A&T State University Greensboro, North Carolina, 27411 and Department of Physics, University of Wisconsin-Madison Madison, Wisconsin, 53706 PACS codes: 05.10. – a; 05.30. – d; 60; 70 Key-words: Quantum NNPDF’s, Generalized Order, Reduced One Particle Phase Space, Free Energy, Slater Sum, Product Property of Slater Sum ∗ ∗ To whom correspondence should be addressed. School of Technology, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411. Phone: (336)334-7718. Fax: (336)334-7546. Email: [email protected]. † North Carolina A&T State University ‡ University of Wisconsin-Madison 1 ABSTRACT The new scheme employed (throughout the “thermodynamic phase space”), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions (QNNPDF’s) are formulated (in a manner analogous to the classical case) to provide a new quantum approach for describing structure at the microscopic level, as well as characterize the thermodynamic properties of material systems. A major point of this paper is that it relates the free energy of an assembly of interacting particles to QNNPDF’s. Also. the methods of this paper reduces to a great extent, the degree of difficulty of the original equilibrium quantum statistical thermodynamic problem without compromising the accuracy of results. Application to the simple case of dilute, weakly degenerate gases has been outlined.. 2 I. INTRODUCTION The new mathematical framework employed in the determination of the exact free energy of pure classical systems [1] (with arbitrary many-body interactions, throughout the thermodynamic phase space), which was recently extended to classical mixed systems[2] is further extended to quantum systems in the present paper.
    [Show full text]
  • Scientific and Related Works of Chen Ning Yang
    Scientific and Related Works of Chen Ning Yang [42a] C. N. Yang. Group Theory and the Vibration of Polyatomic Molecules. B.Sc. thesis, National Southwest Associated University (1942). [44a] C. N. Yang. On the Uniqueness of Young's Differentials. Bull. Amer. Math. Soc. 50, 373 (1944). [44b] C. N. Yang. Variation of Interaction Energy with Change of Lattice Constants and Change of Degree of Order. Chinese J. of Phys. 5, 138 (1944). [44c] C. N. Yang. Investigations in the Statistical Theory of Superlattices. M.Sc. thesis, National Tsing Hua University (1944). [45a] C. N. Yang. A Generalization of the Quasi-Chemical Method in the Statistical Theory of Superlattices. J. Chem. Phys. 13, 66 (1945). [45b] C. N. Yang. The Critical Temperature and Discontinuity of Specific Heat of a Superlattice. Chinese J. Phys. 6, 59 (1945). [46a] James Alexander, Geoffrey Chew, Walter Salove, Chen Yang. Translation of the 1933 Pauli article in Handbuch der Physik, volume 14, Part II; Chapter 2, Section B. [47a] C. N. Yang. On Quantized Space-Time. Phys. Rev. 72, 874 (1947). [47b] C. N. Yang and Y. Y. Li. General Theory of the Quasi-Chemical Method in the Statistical Theory of Superlattices. Chinese J. Phys. 7, 59 (1947). [48a] C. N. Yang. On the Angular Distribution in Nuclear Reactions and Coincidence Measurements. Phys. Rev. 74, 764 (1948). 2 [48b] S. K. Allison, H. V. Argo, W. R. Arnold, L. del Rosario, H. A. Wilcox and C. N. Yang. Measurement of Short Range Nuclear Recoils from Disintegrations of the Light Elements. Phys. Rev. 74, 1233 (1948). [48c] C.
    [Show full text]
  • Statistical Physics for Biological Matter
    springer.com Physics : Biological and Medical Physics, Biophysics Sung, Wokyung Statistical Physics for Biological Matter Provides detailed derivations of the basic concepts for applications to biological matter and phenomena Covers a broad biologically relevant topics of statistical physics, including thermodynamics, equilibrium statistical mechanics, soft matter physics of polymers and membranes, non-equilibrium statistical physics covering stochastic processes, transport phenomena, hydrodynamics, etc Contains worked examples and problems with some solutions This book aims to cover a broad range of topics in statistical physics, including statistical mechanics (equilibrium and non-equilibrium), soft matter and fluid physics, for applications to biological phenomena at both cellular and macromolecular levels. It is intended to be a Springer graduate level textbook, but can also be addressed to the interested senior level 1st ed. 2018, XXIII, 435 p. 1st undergraduate. The book is written also for those involved in research on biological systems or 176 illus., 149 illus. in color. edition soft matter based on physics, particularly on statistical physics. Typical statistical physics courses cover ideal gases (classical and quantum) and interacting units of simple structures. In contrast, even simple biological fluids are solutions of macromolecules, the structures of which are very complex. The goal of this book to fill this wide gap by providing appropriate content Printed book as well as by explaining the theoretical method that typifies good modeling, namely, the Hardcover method of coarse-grained descriptions that extract the most salient features emerging at Printed book mesoscopic scales. The major topics covered in this book include thermodynamics, equilibrium Hardcover statistical mechanics, soft matter physics of polymers and membranes, non-equilibrium ISBN 978-94-024-1583-4 statistical physics covering stochastic processes, transport phenomena and hydrodynamics.
    [Show full text]
  • Statistical Physics University of Cambridge Part II Mathematical Tripos
    Preprint typeset in JHEP style - HYPER VERSION Statistical Physics University of Cambridge Part II Mathematical Tripos David Tong Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 OBA, UK http://www.damtp.cam.ac.uk/user/tong/statphys.html [email protected] –1– Recommended Books and Resources Reif, Fundamentals of Statistical and Thermal Physics • A comprehensive and detailed account of the subject. It’s solid. It’s good. It isn’t quirky. Kardar, Statistical Physics of Particles • Amodernviewonthesubjectwhicho↵ersmanyinsights.It’ssuperblywritten,ifa little brief in places. A companion volume, “The Statistical Physics of Fields”covers aspects of critical phenomena. Both are available to download as lecture notes. Links are given on the course webpage Landau and Lifshitz, Statistical Physics • Russian style: terse, encyclopedic, magnificent. Much of this book comes across as remarkably modern given that it was first published in 1958. Mandl, Statistical Physics • This is an easy going book with very clear explanations but doesn’t go into as much detail as we will need for this course. If you’re struggling to understand the basics, this is an excellent place to look. If you’re after a detailed account of more advanced aspects, you should probably turn to one of the books above. Pippard, The Elements of Classical Thermodynamics • This beautiful little book walks you through the rather subtle logic of classical ther- modynamics. It’s very well done. If Arnold Sommerfeld had read this book, he would have understood thermodynamics the first time round. There are many other excellent books on this subject, often with di↵erent empha- sis.
    [Show full text]
  • Econophysics: a Brief Review of Historical Development, Present Status and Future Trends
    1 Econophysics: A Brief Review of Historical Development, Present Status and Future Trends. B.G.Sharma Sadhana Agrawal Department of Physics and Computer Science, Department of Physics Govt. Science College Raipur. (India) NIT Raipur. (India) [email protected] [email protected] Malti Sharma WQ-1, Govt. Science College Raipur. (India) [email protected] D.P.Bisen SOS in Physics, Pt. Ravishankar Shukla University Raipur. (India) [email protected] Ravi Sharma Devendra Nagar Girls College Raipur. (India) [email protected] Abstract: The conventional economic 1. Introduction: approaches explore very little about the dynamics of the economic systems. Since such How is the stock market like the cosmos systems consist of a large number of agents or like the nucleus of an atom? To a interacting nonlinearly they exhibit the conservative physicist, or to an economist, properties of a complex system. Therefore the the question sounds like a joke. It is no tools of statistical physics and nonlinear laughing matter, however, for dynamics has been proved to be very useful Econophysicists seeking to plant their flag in the underlying dynamics of the system. In the field of economics. In the past few years, this paper we introduce the concept of the these trespassers have borrowed ideas from multidisciplinary field of econophysics, a quantum mechanics, string theory, and other neologism that denotes the activities of accomplishments of physics in an attempt to Physicists who are working on economic explore the divine undiscovered laws of problems to test a variety of new conceptual finance. They are already tallying what they approaches deriving from the physical science say are important gains.
    [Show full text]
  • Lecture Notes for Statistical Mechanics of Soft Matter
    Lecture Notes for Statistical Mechanics of Soft Matter 1 Introduction The purpose of these lectures is to provide important statistical mechanics back- ground, especially for soft condensed matter physics. Of course, this begs the question of what exactly is important and what is less so? This is inevitably a subjective matter, and the choices made here are somewhat personal, and with an eye toward the Amsterdam (VU, UvA, AMOLF) context. These notes have taken shape over the past approximately ten years, beginning with a joint course developed by Daan Frenkel (then, at AMOLF/UvA) and Fred MacK- intosh (VU), as part of the combined UvA-VU masters program. Thus, these lecture notes have evolved over time, and are likely to continue to do so. In preparing these lectures, we chose to focus on both the essential techniques of equilibrium statistical physics, as well as a few special topics in classical sta- tistical physics that are broadly useful, but which all too frequently fall outside the scope of most elementary courses on the subject, i.e., what you are likely to have seen in earlier courses. Most of the topics covered in these lectures can be found in standard texts, such as the book by Chandler [1]. Another very useful book is that by Barrat and Hansen [2]. Finally, a very useful, though more advanced reference is the book by Chaikin and Lubensky [3]. Thermodynamics and Statistical Mechanics The topic of this course is statistical mechanics and its applications, primarily to condensed matter physics. This is a wide field of study that focuses on the properties of many-particle systems.
    [Show full text]
  • Dirty Tricks for Statistical Mechanics
    Dirty tricks for statistical mechanics Martin Grant Physics Department, McGill University c MG, August 2004, version 0.91 ° ii Preface These are lecture notes for PHYS 559, Advanced Statistical Mechanics, which I’ve taught at McGill for many years. I’m intending to tidy this up into a book, or rather the first half of a book. This half is on equilibrium, the second half would be on dynamics. These were handwritten notes which were heroically typed by Ryan Porter over the summer of 2004, and may someday be properly proof-read by me. Even better, maybe someday I will revise the reasoning in some of the sections. Some of it can be argued better, but it was too much trouble to rewrite the handwritten notes. I am also trying to come up with a good book title, amongst other things. The two titles I am thinking of are “Dirty tricks for statistical mechanics”, and “Valhalla, we are coming!”. Clearly, more thinking is necessary, and suggestions are welcome. While these lecture notes have gotten longer and longer until they are al- most self-sufficient, it is always nice to have real books to look over. My favorite modern text is “Lectures on Phase Transitions and the Renormalisation Group”, by Nigel Goldenfeld (Addison-Wesley, Reading Mass., 1992). This is referred to several times in the notes. Other nice texts are “Statistical Physics”, by L. D. Landau and E. M. Lifshitz (Addison-Wesley, Reading Mass., 1970) par- ticularly Chaps. 1, 12, and 14; “Statistical Mechanics”, by S.-K. Ma (World Science, Phila., 1986) particularly Chaps.
    [Show full text]
  • PHAS0103 – Molecular Biophysics (Term 1)
    PHAS0103 – Molecular Biophysics (Term 1) Prerequisites It is recommended but not mandatory that students have taken PHAS0006 (Thermal Physics). PHAS0024 (Statistical Physics of Matter) would be useful but is not essential. The required concepts in statistical mechanics will be (re-)introduced durinG the course. Aims of the Course The course will provide the students with insiGhts in the physical concepts of some of the most fascinatinG processes that have been discovered in the last decades: those underpinning the molecular machinery of the bioloGical cell. These concepts will be introduced and illustrated by a wide ranGe of phenomena and processes in the cell, includinG bio-molecular structure, DNA packinG in the Genome, mechanics of the cytoskeleton, molecular motors and neural siGnalinG. The aim of the course is therefore to provide students with: • KnowledGe and understandinG of physical concepts which are relevant for understandinG bioloGy at the micro- to nano-scale. • KnowledGe and understandinG of how these concepts are applied to describe various processes in the bioloGical cell. Learning Outcomes After completinG this half-unit course, students should be able to: • Give a General description of the bioloGical cell and its contents. • Explain the concepts of free enerGy, entropy and Boltzmann distribution and discuss protein structure, liGand-receptor bindinG and ATP hydrolysis in terms of these concepts. • Explain the statistical-mechanical two-state model, describe liGand-receptor bindinG and phosphorylation as two-state systems and Give examples of “cooperative” bindinG. • Describe how polymer structure can be viewed as the result of random walk, usinG the concept of persistence lenGth, and discuss DNA and sinGle-molecular mechanics in terms of this model.
    [Show full text]