Physics of Life
  Soft and Living Matter Group

Stat-Mech-1


Week-1  :     Class-1         Class-2        Class-3

What is Statistical Physics, How is it related to Thermodynamics ?
How and when did these topics of investigation develop ?

What is Thermodynamics and thermodynamic parameters?
What is heat ? What is equation of state ?
What is equilibrium, as different from steady state ?
Zero-th law of thermodynamics? Why is it important ?
How to fix the Kelvin temperature scale ?

Triple point of water: to set the Kelvin scale.

Using First Law of Thermodynamics to analyze different situations/problems. Internal Energy is a state function. Relation between Cp and Cv for ideal gas. Ideal Gas Law in an adiabatic transformation.
Work done by ideal gas in (i) Adiabatic (ii) Isothermal Transformations.

Week-2 :     Class-4         Class-5        Class-6

What is an engine ? What is a cycle ?
Second Law of Thermodynamics:  What does it add over 1st Law ?
Carnot Engine: Reversible cycle. Why is it important if its an idealized cycle?
Efficiency of Carnot and reversible engines?
Using Carnot Engine to set a temperature scale.
Introduction of Concept of entropy as function of state.

Why does entropy S increase in an irreversible process ?
Why will an irreversible cycle lead to engine efficiency less than a Carnot cycle?
Entropy generation:  Physical meaning  and its consequences.
Entropy maximization to reach equilibrium in   for an "Isolated system".
Helmholtz Free energy F, Gibbs Free energy G: its meaning.
In equilibrium:  Is S maximized?  OR F  minimized ? OR G minimized ?
Should we consider different Thermodyn. pot to analyze diff. scenarios ?   


Class 6 of January 12: Short Overview of Statistical Mechanics:
Microstates, Phase space, configuration space, Concept of Ensemble,
Postulate of Equal Apriori Probability,
Ergodic Hypothesis,
Time average = Ensemble average.
Boltzmann Entropy Formula
Micro-canonical ensemble.

Week-3 :     Class-7          Class-8       Class-9

Class 7 of January 16 : Canonical Ensemble,
Comparision with Micro-canonical :  brief mention of Grand canonical.

Class 8 & 9 : Relating Boltzmann definition of Entropy to  the Thermodynamic concept of Entropy ? Does it have the right properties ?

Starting from expression of Boltzmann Entropy (microscopic) : derive 
expression for Entropy of ideal gas, and derive equation of state of ideal gas.

Class 9 : Properties of Boltzmann Entropy and derivation of PV=nRT from microscopic expression of S

Week 4:  Class-10             Class-11           Class-12

Class 10: Deriving properties of Gases In Microcanonical Ensemble.
Class 11: Gibbs Paradox : Indistinguishable  Particles.
Class 12: Understanding Canonical Ensemble.

Week 5 :    Class 13        Class 14            Class 15A       Class15B

Class  13: Canonical ensemble: Reservoir properties; Energy fluctuations of system.

Class  14: Width ( S.D.) of energy fluctuations.

Class 15 A: Polymer in a heat bath : physical intuition of a system with many degrees of
                     of freedom exchanging energy with reservoir: Canonical system;
                    conformational entropy.
Class 15B: Partition function of Ideal gas,  Derivation of the ideal gas eqn.,
                    Mean energy of the ideal gas in canonical ensemble: Equipartition ?
                    Equipartition theorem: A consequence of the quadratic terms in Hamiltonian.
                    N uncoupled harmonic oscillators who mean positions are fixed in space.

Week 6 : Class 16         Class 17       Class 18A          Class-18B

  Class 16 : Equipartition of Energy ( continued)  
                   Maxwell Boltzmann distribution function of speed of Gas ( speed distribution)
                   MB distribution of one component of the velocity  (velocity distribution)

Class 17: Curie Law and Curie-Weiss Law: Can we get it from Stat-Mech ?
Class 18: Paramagnetic systems : Calculation of <E>, <M>, C_v, chi, and variation with T.


Week 7:           Class 19                 Class 20-A         Class-20 B            

Class 19: Paramagnetism: Micro-canonical ensemble; Negative Temperatures.
Class 20 : Ferromagnetism:  Weiss Mean Field Theory, Obtaining the order-disorder transition and Curie-Weiss Law using Mean Field theory.lass

Week 8 :   Class 21A            Class21B       Class 22      Class 23
Class 23A

Class 21 A,B : General introduction to next Module;  Liouvilles Theorem.
Class 22:  Bacterial DNA organization as a consequence of entropic  repulsion between         internal loops within chromosomes (topologically modified ring polymer).
Class 23, A : Masters Equation and H theorem, Principle of detailed balance.

Week 9 :    Class-24                 Class 25                 Class-26

Class 24: Distribution Function,  Boltzmann Transport Eqn, single relaxation time approx.
Class 25: Calculation of conductivity of Gas of Charged particles : Drude Model.
Class 26: Transport properties; Calc of Viscosity of Gas (microscopic considerations)

Week 10:   Class 27      Class 27A              Class 28                  Class 29

Class 27 : Boltzmann Transport Equation: General form incorporating correlations.
Class 28:  Black body radiation : Planck's Radiation Formula.
Class 29:  Virial Theorem: Expression for the Virial Stress tensor : Calculation of pressure in
                  system of interacting particles.

Week 11:     Class 30                   Class 31                Class 32

Class 30: Equation of state for interacting Gas: Calc of Second Virial Coefficient.
Class 31 : Van-der Waals Equation of state.
Class 32: Grand Canonical Ensemble: Basic Concepts.

Week 12:      Class 33                      Class 34                   Class  35

Class 33: Grand Canonical Ensemble: Calc of thermodynamic quantities.
Class 34:   Fluctuations ( Variance) in number of Particles, Relating fluctuations of
thermodynamic quantities with Response fns; Mention of fluctuation dissipation theorem.
Class 35: Experimental verification of  MB Velocity/speed distribution: Reif  Section 7.12

Weel 13:        Class 36      Class36A     Class36B             Class 37                 Class 38

Class 36 : : Quantum Statistics
Class 36A,B : Distribution functions with  Fermi-Dirac, Bose-Einstein Statistcs;  Degenerate and Non-degenerate quantum gases.
Class  37 : Fermi Distribution function  for Electrons in a metal.
Class 38 :  Debye Theory of Specific Heat of solid at low temperatures.

Week 14 : Wish List
Langevin Equation,