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Entropy
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Entropy

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Entropy[list]

gives the base information entropy of the values in list.

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Entropy[k,list]

gives the base k information entropy.

Details and Options

  • Entropy[string] computes the information entropy of the characters in string.
  • Entropy can handle symbolic data.
  • With the option setting SameTest->f, Entropy[list,…] applies f to pairs of elements in list to determine whether they should be considered equivalent.
  • The default setting for SameTest is SameQ.

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

Entropy of a list of data:

In[1]:=1
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https://wolfram.com/xid/0dqvkcjfkpc-buhmi5
Out[1]=1

Entropy of a symbolic list:

In[1]:=1
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https://wolfram.com/xid/0dqvkcjfkpc-bh23ce
Out[1]=1

Entropy of a string:

In[1]:=1
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https://wolfram.com/xid/0dqvkcjfkpc-cyaad0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqvkcjfkpc-iqpb7i
Out[2]=2

Entropy of a random list of zeros and ones:

In[1]:=1
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https://wolfram.com/xid/0dqvkcjfkpc-dotwsy
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqvkcjfkpc-zwd5k
Out[2]=2

Scope  (1)Survey of the scope of standard use cases

Calculate the entropy of an EventSeries:

In[2]:=2
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https://wolfram.com/xid/0dqvkcjfkpc-1e2x8p
In[3]:=3
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https://wolfram.com/xid/0dqvkcjfkpc-tfcic5
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0dqvkcjfkpc-4wf0h0
Out[4]=4

Applications  (1)Sample problems that can be solved with this function

Calculate the entropy for a path of a TelegraphProcess:

In[7]:=7
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https://wolfram.com/xid/0dqvkcjfkpc-n27fuj
Out[7]=7
In[8]:=8
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https://wolfram.com/xid/0dqvkcjfkpc-0f5e1f
Out[8]=8
In[9]:=9
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https://wolfram.com/xid/0dqvkcjfkpc-4ghk00
Out[9]=9

Neat Examples  (1)Surprising or curious use cases

Entropy of a text:

In[1]:=1
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https://wolfram.com/xid/0dqvkcjfkpc-c3npjl
In[2]:=2
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https://wolfram.com/xid/0dqvkcjfkpc-5i27f
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqvkcjfkpc-gbo4gn
Out[3]=3
Wolfram Research (2008), Entropy, Wolfram Language function, https://reference.wolfram.com/language/ref/Entropy.html.
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Wolfram Research (2008), Entropy, Wolfram Language function, https://reference.wolfram.com/language/ref/Entropy.html.

Text

Wolfram Research (2008), Entropy, Wolfram Language function, https://reference.wolfram.com/language/ref/Entropy.html.

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Wolfram Research (2008), Entropy, Wolfram Language function, https://reference.wolfram.com/language/ref/Entropy.html.

CMS

Wolfram Language. 2008. "Entropy." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Entropy.html.

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Wolfram Language. 2008. "Entropy." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Entropy.html.

APA

Wolfram Language. (2008). Entropy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Entropy.html

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Wolfram Language. (2008). Entropy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Entropy.html

BibTeX

@misc{reference.wolfram_2025_entropy, author="Wolfram Research", title="{Entropy}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Entropy.html}", note=[Accessed: 04-June-2025 ]}

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@misc{reference.wolfram_2025_entropy, author="Wolfram Research", title="{Entropy}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Entropy.html}", note=[Accessed: 04-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_entropy, organization={Wolfram Research}, title={Entropy}, year={2008}, url={https://reference.wolfram.com/language/ref/Entropy.html}, note=[Accessed: 04-June-2025 ]}

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@online{reference.wolfram_2025_entropy, organization={Wolfram Research}, title={Entropy}, year={2008}, url={https://reference.wolfram.com/language/ref/Entropy.html}, note=[Accessed: 04-June-2025 ]}