Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Statistical Mechanics online course offers a fundamental understanding of statistical mechanics and thermodynamics. It begins with the basic concepts of thermodynamics and takes on statistical mechanics principles towards the end. The program does mandate any prior exposure to the topics.
The Statistical Mechanics course syllabus covers topics like laws of thermodynamics, entropy, types of canonical ensemble, the theory of probability, and quantum mechanics. The program is a core course in the Physics discipline. Over the 12 weeks, you will be provided with high-quality video lectures delivered by Prof. Dipanjan Chakraborty.
IISER Mohali provides the Statistical Mechanics certification course in conjunction with Swayam. If you wish, you can also opt for the digital course certificate issued by Swayam. This certificate can be easily attached to your CV and LinkedIn profile. However, you will have to register for an exam by paying the requisite fee and pass the test to receive the e-certificate.
The Highlights
- Comprehensive curriculum
- AICTE-approved FDP training
- Free admission
- Verifiable e-certificate
- Undergraduate/Postgraduate- level program
- IISER Mohali’s syllabus
- Experienced faculty
- Payable certification exam
Programme Offerings
- experienced faculty
- Verifiable e-certificate
- Undergraduate/Postgraduate- level program
- Payable certification exam
- Comprehensive curriculum
- IISER Mohali’s syllabus
- Free Admission
- AICTE-approved FDP training
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IISER Mohali |
You aren’t required to pay any Statistical Mechanics program fees to access the course. However, the mandatory payment of Rs. 1,000 is required for Swayam’s proctored test registration.
The statistical Mechanics fee structure
Program Type | Fees |
Statistical Mechanics | FREE |
Statistical Mechanics – examination | Rs. 1,000 |
Eligibility Criteria
If you are looking to join the Statistical Mechanics program, you must have an elementary knowledge of quantum mechanics, mathematical methods, and classical mechanics.
Certificate Qualifying Details
Furthermore, a minimum of 40% score in both final exams and assignments (best of eight) is required if you want to receive the e-certificate by Swayam. Your assignment score (average) should also be >= 10/25, whereas the exam (final) score must be >= 30/75. For calculation, 25% of assignment evaluation, (computing 8 high-scoring assignments), and 75% of your exam result is used.
What you will learn
The Statistical Mechanics online training by Swayam will enable you to display expertise in these concepts:
- Quantum mechanics
- Theory of Probability
- Types of Canonical Ensemble
- Bosons and Fermions
- N-particles
- Laws of thermodynamics
Who it is for
The Statistical Mechanics online course is ideal for:
- BSc/MSc students
- First-year Ph.D. students
- BS/MS students
Admission Details
Step 1 - Go through the Statistical Mechanics course details by visiting https://onlinecourses.nptel.ac.in/noc21_ph09/preview
Step 2 - Next, choose the ‘Sign in/Register’ option to sign up or sign in for this training course.
Step 3 - You can sign-in directly if you have existing Swayam credentials. If not, create new ones by furnishing the required details.
Step 4 - Lastly, click on the ‘send verification code’ button to activate your ID.
Step 5 - Use the code sent to your registered email address to finish account creation and enrolment.
Application Details
There’s no dedicated Statistical Mechanics certification program application form, per se. You can join this online training by providing an email, username, and password. Alternatively, an existing Google, Facebook, Swayam, and Microsoft ID can be used for registration too. Educational details, work experience information, and additional contact information must be provided while creating an account.
The Syllabus
- Introduction to Thermodynamics – the idea of macroscopic and microscopic variables with examples: a classical ideal gas and a magnetic spin system. Description of a thermodynamic system and the choice of macroscopic variables. Connection with statistical mechanics.
- Zeroth law of thermodynamics: The concept of empirical temperature arising from the zeroth law.
- First law and perpetual machines of first kind. Concept of exact and inexact differentials (for example heat and work). Similarity with the conservation of mechanical energy. Introduction of generalized forces and generalized coordinates in a thermodynamic system. The idea of response functions and their measurements.
- Second law of thermodynamics: Concepts of heat engines. Carnot engine and its efficiency. Relation with empirical temperature. Kelvin and Clausius statement of second law and their equivalence. Clausius theorem and its proof. First, second and third TdS equations.
- Extensive property of Entropy and Internal Energy. Euler theorem and Gibbs-Duhem relation from this. Illustration of Gibbs-Duhem relation for an ideal gas. Partial derivatives.
- Legendre transformations and thermodynamic free energies. Their application in real life. Introduction to Jacobians and Maxwell’s relation. Use of Jacobians in deriving thermodynamic relations. Relation between specific heats.
- Stability criteria for thermodynamic systems. Concavity of entropy and convexity of internal energy. Consequence of concavity of entropy and convexity of internal energy – constraints on response functions.
- Brief introduction to theory of probability. Rules of probability. Interpretation of probability based on symmetry or frequency. Conditional probability – its interpretation in terms of sample space. Partition theorem and Bayes theorem.
- Examples of probability distribution – discrete distributions such as Binomial and Poisson. Continuous probability densities – introduction to a random variable. Normal distribution. Correlation functions. Generating functions. Central limit theorem. Example of a random walk on discrete lattice. Information and uncertainty – connection with statistical mechanics.
- Microcanonical Ensemble: Concept of classical probability density – Liouville equation, incompressible flow in phase space, meaning of ensemble average and time average of a physical quantity, ergodic theory. Equal probability and the microcanonical ensemble. Connection with thermodynamics. Counting of states – discrete case and continuous random variables.
- Canonical ensemble: Understanding what is a canonical ensemble and why we need it – connecting it with thermodynamics. Derivation of the probability density in the canonical ensemble. Fluctuations and their significance – positivity of the response functions. Examples of non-interacting systems. Equipartition theorem.
- Grand canonical ensemble. Probability density in grand canonical ensemble. Fluctuations and their significance. Generator of canonical ensemble.
- Quantum statistical mechanics: concept of averages in quantum stat. mech. Mixed and pure states and definition of density matrix. Density operators in quantum stat. mech. For different ensembles. Canonical density matrix for single particle. Wigner transformation. Examples with free particle and harmonic oscillator.
- N-particle wavefunction and canonical density matrix for N-particles. Concept of symmetric and anti-symmetric wave functions – symmetry and permutation operator. Their eigenvalues. Determination of the normalization of symmetric and anti-symmetric wave functions. Calculation of the N-particle canonical partition function for a system of ideal gas. Second virial coefficient and pair-interaction in an ideal gas.
- Grand canonical formulation of non-interacting Fermions and Bosons. Thermodynamic quantities in terms of Fermi and Bose integrals. High temperature expansion of a Fermi gas. Degenerate Fermi gas. Low temperature expansion and thermodynamic quantities at low temperature.
- Bosons: The ideal Bose gas and derivation of thermodynamic quantities in terms of Bose integrals. Bose-Einstein condensation. Specific heat of a Bose gas. Harmonically trapped Bose gas.
Evaluation process
Your certification eligibility for the Statistical Mechanics course is evaluated based on your performance in the assignments and the final exam. You can register for the final exam by paying Rs. 1,000. The exam will be held in one of Swayam’s designated exam centers. You will be provided with the option to choose the exam center depending on your convenience. The test will be proctored.
Instructors
IISER Mohali Frequently Asked Questions (FAQ's)
You can use this link: http://nptel.ac.in/noc to validate your certification.
This course falls under the Physics discipline.
No, the final exam is a proctored test, which requires you to be present in person.
No, the Statistical Mechanics online training doesn’t provide industry support.
The program duration is 12 weeks.