Mixing
Tsallis entropy limit
I'm trying to understand how Tsallis entropy generalizes Boltzmann-Gibbs entropy. The Tsallis Entropy wikipedia article says Tsallis entropy of a distribution $p_i$ is:
$$
s_q(p_i) = frac{k}{q-1} left( 1 - sum_i p^q_i right) ;~~~~~~~~ q > 0
$$
And that taking the limit as $q rightarrow 1$ we recover the Botlzmann-Gibbs entropy:
$$
lim_{q rightarrow 1} S_q = S_{BG} = -k sum_i p_i ln p_i
$$
How does one actually take this limit though? I'm not sure how to factor / deal with the $k/(q-1)$ term.
Thank you,
limits entropy
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
add a comment |
I'm trying to understand how Tsallis entropy generalizes Boltzmann-Gibbs entropy. The Tsallis Entropy wikipedia article says Tsallis entropy of a distribution $p_i$ is:
$$
s_q(p_i) = frac{k}{q-1} left( 1 - sum_i p^q_i right) ;~~~~~~~~ q > 0
$$
And that taking the limit as $q rightarrow 1$ we recover the Botlzmann-Gibbs entropy:
$$
lim_{q rightarrow 1} S_q = S_{BG} = -k sum_i p_i ln p_i
$$
How does one actually take this limit though? I'm not sure how to factor / deal with the $k/(q-1)$ term.
Thank you,
limits entropy
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
add a comment |
I'm trying to understand how Tsallis entropy generalizes Boltzmann-Gibbs entropy. The Tsallis Entropy wikipedia article says Tsallis entropy of a distribution $p_i$ is:
$$
s_q(p_i) = frac{k}{q-1} left( 1 - sum_i p^q_i right) ;~~~~~~~~ q > 0
$$
And that taking the limit as $q rightarrow 1$ we recover the Botlzmann-Gibbs entropy:
$$
lim_{q rightarrow 1} S_q = S_{BG} = -k sum_i p_i ln p_i
$$
How does one actually take this limit though? I'm not sure how to factor / deal with the $k/(q-1)$ term.
Thank you,
limits entropy
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
I'm trying to understand how Tsallis entropy generalizes Boltzmann-Gibbs entropy. The Tsallis Entropy wikipedia article says Tsallis entropy of a distribution $p_i$ is:
$$
s_q(p_i) = frac{k}{q-1} left( 1 - sum_i p^q_i right) ;~~~~~~~~ q > 0
$$
And that taking the limit as $q rightarrow 1$ we recover the Botlzmann-Gibbs entropy:
$$
lim_{q rightarrow 1} S_q = S_{BG} = -k sum_i p_i ln p_i
$$
How does one actually take this limit though? I'm not sure how to factor / deal with the $k/(q-1)$ term.
Thank you,
limits entropy
limits entropy
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
edited Nov 21 '18 at 22:45
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
asked Nov 21 '18 at 0:40
aaronsnoswell
1618
1618
add a comment |
add a comment |
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