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statistical mechanics

Zhigang Suo's picture

Freely jointed chain

A single strand of polymer is a chain of a large number of monomers.  The monomers are joined by covalent bonds, and two bonded monomers may rotate relative to each other.  At a finite temperature, the polymer rapidly changes from one configuration to another.  When the two ends of the polymer are pulled by a force, the distance between the two ends changes.  The polymer is known as an entropic spring.  These notes are developed as part of statistical thermodynamics to supplement the course on advanced elasticity

Open Postdoctoral Position at Carnegie Mellon University (USA)

We are currently looking for a top candidate to join the System Level Design group at CMU (www.ece.cmu.edu/~sld/), as a Postdoctoral Associate, starting Spring 2013. Main responsibilities involve work on modeling and control of stochastic micro-robotic swarms targeting biological applications.

Amit Acharya's picture

Microcanonical Entropy and Mesoscale Dislocation Mechanics and Plasticity

(Journal of Elasticity, Carlson memorial Volume)

A methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define the dissipative driving-force and energetic fields in continuum thermomechanics. A thermodynamic model of dislocation mechanics is discussed. One outcome is a definition for the mesoscale back-stress tensor and the symmetric, polar dislocation density-dependent, Cauchy stress tensor from atomistic ingredients.

Zhigang Suo's picture

Free Energy

For a system in thermal contact with the rest of the world, we have described three quantities: entropy, energy, and temperature. We have also described the idea of a constraint internal to the system, and associated this constraint to an internal variable.

Cai Wei's picture

Lecture notes on "Elasticity" and "Statistical Mechanics"

The lecture notes of the two courses I taught at Stanford University during the last two quarters, "ME 340 Elasticity" and "ME 334 Introduction to Statistical Mechanics", are available in PDF format online at:

  http://micro.stanford.edu/~caiwei/me340/

  http://micro.stanford.edu/~caiwei/me334/

Perhaps it could be useful to you.

Ajit R. Jadhav's picture

What is "randomness"?

Does the word "randomness" have antonym? If yes, what is it? Why? What view of randomness does that imply?

Ajit R. Jadhav's picture

A book on mechanics that would pique your curiosity

I am happy to recommend the following book for your general reading.

Ranganath, G.S., ``Mysterious Motions and other Intriguing Phenomena in Physics," Hyderabad, India: Universities Press (2001)

Zhigang Suo's picture

Electric potential

  • Electric charge
  • Movements of charged particles
  • Elastic dielectric
  • Work done by a battery and by a weight
  • Electromechanical coupling
  • Conservative system
  • Experimental determination of electric potential
  • Lagendre transformation
  • parallel-plate capacitor

Return to the outline of Statistical Mechanics

Zhigang Suo's picture

Chemical potential

  • A system that can exchange particles with the rest of the world
  • Chemical potential
  • Ideal gas
  • Experimental determination of chemical potential
  • Lagendre transformation
  • Ideal gas once more
  • Experimental determination of chemical potential
  • A system in contact with a reservoir of energy, volume and particles
  • A kinetic model

Return to the outline of Statistical Mechanics

Zhigang Suo's picture

Pressure

So far we have been mainly concerned with systems of a single independent variable: energy (node/4878). We now consider a system of two independent variables: energy and volume. A thermodynamic model of the system is prescribed by entropy as a function of energy and volume.

The partial derivatives of the function give the temperature and the pressure. This fact leads to an experimental procedure to determine the function for a given system.

The laws of ideal gases and osmosis are derived. The two phenomena illustrate entropic elasticity.

Zhigang Suo's picture

The Boltzmann Distribution

  • A small system in thermal contact with a large system
  • The Boltzmann factor
  • Partition function
  • The probability for a system in thermal equilibrium with a reservoir to be in a specific state
  • The probability for a system in thermal equilibrium with a reservoir to be in a configuration
  • Thermal fluctuation of an RNA molecule
  • A matter of words

Return to the outline of Statistical Mechanics.

Zhigang Suo's picture

Entropy

  • A dissection of a sample space
  • Entropy of a dissection of a sample space
Zhigang Suo's picture

Energy and Fundamental Postulate

We have described two great principles of our world: the fundamental postulate and the conservation of energy. The former is the foundation of thermodynamics, as we have learned in a previous lecture. The latter is not specific to thermodynamics: we borrow the concept of energy—along with the principle of the conservation of energy—from other branches of science, such as mechanics and electrodynamics. Both principles are abstracted from many empirical observations.

Zhigang Suo's picture

Fundamental postulate. Entropy

Of our world the following facts are known:

  • An isolated system has a set of quantum states.
  • The isolated system ceaselessly flips from one quantum state to another.
  • A system isolated for a long time is equally probable to be in any one of its quantum states.

Thus, an isolated system behaves like a fair die. The following notes remind you what an isolated system is, and translate the theory of probability of rolling a fair die to the thermodynamics of an isolated system.

Zhigang Suo's picture

Probability

  • An experiment that has many possible outcomes
  • Construct a sample space at a suitable level of detail
  • Probability of an event
  • Conditioning
  • Independent events
  • Random variable
  • Use a random variable to specify an event
  • Use a random variable to dissect a sample space
  • Probability distribution of a random variable
  • Variance of a random variable
  • A dimensionless measure of the fluctuation of a random variable

Return to the outline of Statistical Mechanics

Zhigang Suo's picture

A Fresh Look at a Beautiful Subject

This is a review on Thermal Physics by Charles Kittle and Herbert Kroemer. I posted the review on Amazon on 2 December 2001.

This is by far THE BEST textbook on the subject. As many people say, thermodynamics is a subject that one has to learn at least three times. I can easily understand the very negative review from the undergraduate student at Berkely. The subject itself is hard, and simply is not for everyone, not for the first run at least. I say this from experience. I earned a Ph.D. degree over ten years ago, and took courses on thermodynamics at both undergraduate and graduate levels. I didn't understand the subject at all, and didn't find much use in my thesis work. However, something about the subject has kept me going back to it ever since. I now own about 40 books on the subject, and use the ideas almost daily in my research.

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