Lecture1Jan26

Lecture1Jan26 - Key Concepts a Statistical Ensembles b...

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Key Concepts: a) Statistical Ensembles b) Averages c) Self-Averaging Reading: Reif, Ch1
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What is it all about? Thermodynamics: Study of Macroscopic Properties (like, heat, temperature, energy, volume, pressure) of large, bulk systems, such as materials, heat machines etc. Was founded in 18th Century in the course of Industrial revolution (Carnot, Cuviet,Clapeiron, Clausius, Boyle, Fourier, Fick etc). Agnostic about underlying microscopic causes of observed phenomena (e.g. for many years the dominant paradigm in thermodynamics was theory of Flogiston which asserted that heat is a special liquid which flows from a hot object to a cold one. Statistical Mechanics (from end of 19th century till present - Maxwell, Boltzmann, Gibbs, Landau, Feinmann, Onsager, Ulam…) seeks to describe the same macroscopic properties but with microscopic, molecular picture! Statistical mechanics is predictive: it can successfully derive many important properties of materials (heat capacity, susceptibility, even protein structure and stability!) from properties of their constituent atoms and molecules.
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The beauty and power of Statistical Mechanics • Statistical mechanics helps us to understand - and predict - properties of many systems as diverse as: A) Materials - deriving and designing mechanical, thermal and other properties from molecular structure B) Biology - predicting protein structure, stability, interactions from DNA sequences. Bridging time scales in Biology - from atoms to organisms (see next slide) C) Other complex phenomena - earthquakes, polling and elections, financial markets - Statistical Mechanics ideas give very powerful tools to analyze these diverse phenomena. You will see how these ideas work as we progress…
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What does Statistical Mechanics Study? Large systems (number of particles in the range 10 2 -10 23 ) Average properties - like temperature, heat capacity, density, pressure etc…. Equilibrium properties - time independent quantities which settled over long time scales. OR- Non-equilibrium properties - evolving with time. Example: At t=0 the partition is removed The system starts to evolve with Time, pressure is continuously changing Finally at longer times the system settles at new equilibrium and with new pressure.
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How is that possible? Classical or Quantum Mechanics: One particle - easy (linear oscillator, motion of a planet around the sun, hydrogen atom - different approaches in quantum and classical mechanics but still very doable Two particles - possible but much harder Three particles - VERY tough Four particles - almost impossible (analytically, but can be simulated well with modern computers) Now we are talking about 10 23 particles - are we crazy????
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Many particles - Easy again! Why?
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This note was uploaded on 05/04/2010 for the course CHEM 161 taught by Professor Shaklovich during the Spring '10 term at Harvard.

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Lecture1Jan26 - Key Concepts a Statistical Ensembles b...

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