4. Tsallis entropy is given as: kB Sa = - (q-1) (1-jp) Where, q is an...

 

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4. Tsallis entropy is given as: kB Sa = - (q-1) (1-jp) Where, q is an index of extensivity. By changing the value of q different types of distributions can be obtained. 1. Show that the above distribution becomes Gibbs Boltzmann entropy when q 1, The Gibbs-Boltzmann entropy: S - jp;log (pj) Hint: Take the case of a coin toss problem and calculate Tsallis entropy for a few values of q (e.g., 0.999, 0.75, 0.5) as a function of pj, by varying it from 0 to 1. Do the same for Gibbs Boltzmann entropy. Now plot both the entropies as a function of pj. 4. Tsallis entropy is given as: kB Sa = - (q-1) (1-jp) Where, q is an index of extensivity. By changing the value of q different types of distributions can be obtained. 1. Show that the above distribution becomes Gibbs Boltzmann entropy when q 1, The Gibbs-Boltzmann entropy: S - jp;log (pj) Hint: Take the case of a coin toss problem and calculate Tsallis entropy for a few values of q (e.g., 0.999, 0.75, 0.5) as a function of pj, by varying it from 0 to 1. Do the same for Gibbs Boltzmann entropy. Now plot both the entropies as a function of pj.