Material for Statistical physics for 2014/2015 is on the TCD Blackboard. Below is the contents for Statistical Physics I (MA2342) for 2013.

### Tutorials

• Tutorial 1(Nov 15,20,22,27): Foundations of statistical physics and relevant mathematics
• Solution to tutorial, part 7:
• Tutorial 2(Dec 4): Van-der-Waals gas and first order phase transitions , Figures 1 and 2:
• Solution to tutorial 2:

### Home Work

• When to submit and how home work is assessed
• Please put this cover page on top of each problem set that you submit:
• Notations, conventions, tables etc:
• Problem sets:
1. Thermodynamic relations (theory)
2. Ideal gas
3. Thermodynamic relations (practice)
4. Entropy and related paradoxes . Try yourself as Maxwell's demon here, here, or here .
5. Calculus
6. Classical relativistic gas
7. Polyatomic ideal gas
8. Systems with interactions, virial expansion
9. Easy (but important) HW
10. Entropy, Combinatorics, Probability

### Solutions and comments to Home Work

 I II III IV V VI VII VIII IX X
Mathematica nb for HW IV solution:

### Topics for exam

Exam will be 70%-80% of practical questions, and 20%-30% of theory.

• For the theoretical questions, I will ask only those ones that were explained during lectures. For most of them, theory in the amount of K.Huang book "Introduction to Statistical Physics" is enough.
• For the practical questions, they will be very similar, though not fully equivalent, to those asked in tutorials and home works (non-starred ones).
• The best and very fruitful way to prepare is to study solutions to home works and tutorials.

• Mathematics: Gaussian integral. Gamma function (definition). Method of Lagrange multiplier. Legendre transform. Some elements of combinatorics and probability theory. Central limit theorem. Explicit examples of central limit theorem: averaging over dice rolls, random walk (HW 9.6). Volume of n-dimensional ball, area of (n-1)-dimensional sphere.
• Corresponding HW's: V,X, and partially IX.

• No theoretical questions like "what is the method of Lagrange multiplier" will be asked. No questions like "what is the value of integral" will be asked either. But the mentioned mathematical techniques might be needed for solve certain exam questions.

Duration of exam is 2 hours. Exam will consist of 4 questions. You should solve 3 of your choice to get the full score.

1 question will be devoted to the topics from:

• Thermodynamics: Extensive and intensive quantities. Laws of thermodynamics. Reversible and irreversible processes, 2nd law of thermodynamics in various formulations. Entropy. Thermodynamic potentials. Maxwell relations. Response functions (heat capacity, compressibility etc) and relations between them. Thermodynamic definition of the temperature. Carnot heat engine.
• Ideal gas: Thermodynamic properties (entropy, free energy, energy, response functions etc). Adiabatic process. Efficiency of heat engines.
• Examination may include systems that are different from ideal gas (e.g. magnetic systems). Their thermodynamic relations are derived in full analogy (sometimes, even just by renaming some quantities) and you are expected to be able to do such derivations if basic information about a thermodynamic system is given.
• Corresponding HW's: HW1,HW2,HW3.

2 questions will be devoted to the topics from:

• Foundations of statistical physics: Laplace determinism. Chaos (in particular, example of Lorenz attractor). Averaging over time and averaging over statistical ensemble. Liouville's theorem. Ergodic hypothesis (and why it is not enough or not necessarily required). Maxwell distribution (with derivation). Mean and square mean velocities of the particles. Central limit theorem. Bernoulli process (coin tossing, in particular limit of very many coin tosses). Importance of subsystem's clustering for applicability of statistical physics. Types of observables studied by statistical physics. Statistical definition of entropy. Discussion of Boltzmann H-teorem (HW4, first part). Time arrow.
• Microcanonical, canonical, grand canonical ensembles for discrete and continuous systems: derivation and main properties. Partition function. Physical interpretation for the measure of integration to compute partition function. Deriving thermodynamics from statistical ensembles. Examples: classical ultra-relativistic gas (HW6), monoatomic ideal gas (tutorial 1).
Grand thermodynamic potential. Chemical potential
• Corresponding HW's: IV,VI,IX, tutorial 1.

1 question will be devoted to the topics from:

• Polyatomic ideal gas. Equipartition theorem. Systems with non-conserved number of particles. Euler identity. Systems with interaction. Virial expansion. Van-der-Waals gas. Phase diagrams gas-liquid, critical point. Phase transitions of first order. Clausius-Clapeyron equation. Phase diagrams gas-liquid-solid. Triple point.
• Corresponding HW's: VII,VII, tutorial 2.

### Example of exam

Profit from having an example! Do not look the sample exam questions immediately. First study solutions to HW's, tutorials, and a bit of theory. Then allocate 2 hours and give it a try.