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<p style="margin-top:0;margin-bottom:0">Hi FISers,</p>
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</p>
<p style="margin-top:0;margin-bottom:0">I found a typo in the legend to Figure 1 in my last post: ".. . . without energy dissipation, no energy, . . ." shoud read <br>
<br>
"<span style="color: rgb(255, 0, 0);">Without energy dissipation, no information.</span>" (4).</p>
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<p style="margin-top:0;margin-bottom:0">In fact, Statement (4) may be fundamental to informatics in general so that it may be referred to as the "<span style="color: rgb(255, 0, 0);">First Principle of Informatics" (FPI).</span></p>
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<p style="margin-top:0;margin-bottom:0">If this conjecture is correct, FPI may apply to the controversioal interpretations of the wavefunction of a material system (WFMS), since WFMS is supposed to encode all the information we have about the material system
under consideration and hence implicates "information". It thus seems to me that the complete interpretation of a wavefucntion, according to FPI, must specify the selection process as well, i.e., the free energy-dissipating step, which I am tempted to identified
with "measurement" , "quantum jump", or "wavefunction collapse". </p>
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<p style="margin-top:0;margin-bottom:0">I am not a quantum mechanician, so it is possible that I have committed some logical errors somewhere in my arguemnt above. If you diectect any, please let me know.</p>
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<p style="margin-top:0;margin-bottom:0">With All the best.</p>
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<p style="margin-top:0;margin-bottom:0">Sung</p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Fis <fis-bounces@listas.unizar.es> on behalf of Sungchul Ji <sji@pharmacy.rutgers.edu><br>
<b>Sent:</b> Sunday, June 3, 2018 12:13:11 AM<br>
<b>To:</b> 'fis'<br>
<b>Subject:</b> [Fis] The information-entropy relation clarified: The New Jerseyator</font>
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<p style="margin-top:0; margin-bottom:0">Hi FISers,</p>
<p style="margin-top:0; margin-bottom:0"><br>
</p>
<p style="margin-top:0; margin-bottom:0">One simple (and may be too simple) way to distinguish between
<i>information </i>and <i>entropy</i> may be as follows:</p>
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<p style="margin-top:0; margin-bottom:0">(i) Define information (I) as in Eq. (1)</p>
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</p>
<p style="margin-top:0; margin-bottom:0"> I = -log_2(m/n) = - log_2 (m) + log_2(n) (1)</p>
<p style="margin-top:0; margin-bottom:0"><br>
</p>
<p style="margin-top:0; margin-bottom:0">where n is the number of all possible choices (also called variety) and m is the actual choices made or selected. </p>
<p style="margin-top:0; margin-bottom:0"><br>
</p>
<p style="margin-top:0; margin-bottom:0">(ii) Define the negative binary logarithm of n, i.e., -log_2 (n), as the 'variety' of all possible choices and hence identical with Shannon entropy H, <span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">as
suggested by Wicken [1]. Then Eq. (1) can be re-writtens as Eq. (2):</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"> I = - log_2(m) -
H (2) </span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">(iii) It is evident that when m = 1
(i.e., when only one is chosen out of all the variety of choices available) , Eq. (2) reduces to Eq. (3):</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"> I = - H
(3)</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">(iv) As is well known, Eq. (3) is the
basis for the so-called the "negentropy priniciple of Information" frist advocated by Shroedinger followed by Brillouin,and others. But Eq. (3) is clearly not a principle but a special case of Eq. (2) with m = 1. </span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">(v) In conlcusion, I claim that information
and negative entropry are not the same qualitatively nor quantiatively (except when m = 1 in Eq. (2)) and represent two opposite nodes of a fundamental triad [2]:</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"> </span></p>
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</span></p>
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<p style="margin:0in; margin-bottom:.0001pt; background:white"><span style="font-family:"Calibri",sans-serif; color:black"> Selection </span></p>
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<span style="font-family:"Calibri",sans-serif; color:black"> H ---------------------------------------------------------------->
<b style="">I</b> <br>
(uncertainty before selection) <span style="">
</span> (Uncertainty after selection)</span></p>
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<p style="margin:0in; margin-bottom:.0001pt; background:white"><b><span style="font-family:"Calibri",sans-serif; color:black">Figure 1. </span></b><span style="font-family:"Calibri",sans-serif; color:black"> The New Jerseyator model of information (NMI) [3].<span style="">
</span>Since selection requires free energy dissipation, NMI implicates both information and energy.<span style="">
</span>That is, without energy dissipation, no energy, and hence NMI may be viewed as a self-organizing process (also called dissipative structure) or an ‘-ator’.
<span style=""> </span>Also NMI is consistent with “uncertainty reduction model of information.”
<span style=""> </span></span></p>
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<br>
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<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">With all the best.</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">Sung</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">P.s. There are experimetnal evidences
that informattion and entropy are orthogonal, thus giving rise to the <i>Planck-Shannon plane</i> that has been shown to distiguish between cancer and healthy cell mRNA levels. I will discus this in n a later post. </span></p>
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<p style="margin-top:0; margin-bottom:0">References:</p>
<p style="margin-top:0; margin-bottom:0"> [1] Wicken, J. S. (1987). Entropy and information: suggestions for common language. <i>Phil. Sci.</i>
<b>54</b>: 176=193. <br>
[2] Burgin, M (2010). <i>Theory of Information: Funadamentality, Diversity, and Unification</i>. World Scientific Publishing, New Jersey,</p>
<p style="margin-top:0; margin-bottom:0"> [3] Ji, S. (2018). <i>The Cell Langauge theory: Connecting Mind and Matter.</i> World Scientific Publishing, New Jersey. Figure 10.24.</p>
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