Tsallis entropy, proposed by C. Tsallis in 1988, is seen as a generalization of the conventional Boltzmann-Gibbs entropy. Since its inception, Tsallis-like distributions, which can be obtained from generalized entropy, have been successfully used in many branches of natural and social sciences. Lately, it has been seen that particle distributions produced in high-energy collision experiments (at the Large Hadron Collider and Relativistic Heavy Ion Collider) are well-described by the Tsallis-like power-law distributions. In this project, physical conditions giving rise to this power-law behavior will be revisited. Next, Tsallis thermodynamic variables using the Tsallis distributions will be calculated to study their applications in the field of high-energy collisions.

Tasks

1. A brief review of the Tsallis statistical mechanics and related literature. 2. Tsallis-like phenomenological distributions and their connection with the Tsallis statistical mechanics. 3. Calculating Tsallis thermodynamic variables in classical and quantum cases. 4. Applications of the Tsallis thermodynamic variables in the field of high energy collision. 5. Reviewing results and preparing a draft of the report.

Preliminary schedule by topics/tasks

Week 1: A brief review of the Tsallis statistical mechanics and related literature. Week 2: Learning about the Tsallis-like phenomenological distributions and their connection with the Tsallis statistical mechanics. Weeks 3-4: Calculating Tsallis thermodynamic variables for gases of massless and slightly massive classical and quantum particles. Week 5: Applications of the obtained results in the field of high energy collision. Week 6: Reviewing results and preparing a report.

Required skills

Thorough knowledge of thermodynamics and statistical mechanics is required. Basic level familiarity with Mathematica will be an added advantage. Familiarity with LaTeX is necessary.

Acquired skills and experience

Participants will be familiar with the basic formulations of the Tsallis statistical mechanics and their applications in the field of high-energy collisions, which is a very contemporary research topic. They are also expected to increase their skills in performing symbolic computations using Mathematica.

Recommended literature

1. C Tsallis, Introduction to non extensive statistical mechanics, Springer Science+Business Media (2009). 2. G. Wilk, and Z. Wlodarczyk, Interpretation of the Nonextensivity Parameter q in Some Applications of Tsallis Statistics
and Levy Distributions, Phys. Rev. Lett. 84 (2000) 2770. 3. J. Cleymans, D. Worku, Relativistic thermodynamics: Transverse momentum distributions in high-energy physics, Eur. Phys. J. A 48 (2012) 160.