Jump to navigation Jump to search

General

Display information for equation id:math.2355.12 on revision:2355

* Page found: Prüfungsfragen:Statistische Physik (eq math.2355.12)

(force rerendering)

Occurrences on the following pages:

Hash: 9c0676725b62884c4c6ab5d29c28bef6

TeX (original user input):

S:=-k \left\langle \operatorname{ln} \rho \right\rangle =-k \operatorname{Tr} \left(\operatorname{ln} \rho  \right\rangle= -k\sum_\alpha p_\alpha \operatorname{ln} p_\alpha

TeX (checked):

S:=-k\left\langle \operatorname {ln} \rho \right\rangle =-k\operatorname {Tr} \left(\operatorname {ln} \rho \right\rangle =-k\sum _{\alpha }p_{\alpha }\operatorname {ln} p_{\alpha }

LaTeXML (experimental; uses MathML) rendering

MathML (5.54 KB / 1.073 KB) :

S := - k ln ρ = - k Tr ( ln ρ = - k α p α ln p α fragments S assign k fragments ln ρ k Tr fragments ( ln ρ k subscript 𝛼 subscript 𝑝 𝛼 ln subscript 𝑝 𝛼 {\displaystyle{\displaystyle S:=-k\left\langle\operatorname{ln}\rho\right% \rangle=-k\operatorname{Tr}\left(\operatorname{ln}\rho\right\rangle=-k\sum_{% \alpha}p_{\alpha}\operatorname{ln}p_{\alpha}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle S:=-k\left\langle\operatorname{ln}\rho\right%&#10;\rangle=-k\operatorname{Tr}\left(\operatorname{ln}\rho\right\rangle=-k\sum_{%&#10;\alpha}p_{\alpha}\operatorname{ln}p_{\alpha}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">S</mi>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">:=</mo>
      <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">-</mo>
      <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">k</mi>
      <mrow id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
        <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml"></mo>
        <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">ln</mi>
        <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">ρ</mi>
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml"></mo>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
      <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">-</mo>
      <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">k</mi>
      <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">Tr</mi>
      <mrow id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
        <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">(</mo>
        <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">ln</mi>
        <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">ρ</mi>
        <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml"></mo>
      </mrow>
      <mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">=</mo>
      <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">-</mo>
      <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">k</mi>
      <mstyle displaystyle="true" id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">
        <munder id="p1.1.m1.1.32a" xref="p1.1.m1.1.32.cmml">
          <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml"></mo>
          <mi id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">α</mi>
        </munder>
      </mstyle>
      <msub id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">
        <mi id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">p</mi>
        <mi id="p1.1.m1.1.27.1" xref="p1.1.m1.1.27.1.cmml">α</mi>
      </msub>
      <mi id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">ln</mi>
      <msub id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">
        <mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">p</mi>
        <mi id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">α</mi>
      </msub>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">S</csymbol>
        <csymbol cd="latexml" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">assign</csymbol>
        <minus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
        <csymbol cd="unknown" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">k</csymbol>
        <cerror id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
          <csymbol cd="ambiguous" id="p1.1.m1.1.2a.cmml" xref="p1.1.m1.1.2">fragments</csymbol>
          <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"></ci>
          <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">ln</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">ρ</csymbol>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"></ci>
        </cerror>
        <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
        <minus id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12"/>
        <csymbol cd="unknown" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">k</csymbol>
        <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">Tr</ci>
        <cerror id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
          <csymbol cd="ambiguous" id="p1.1.m1.1.7a.cmml" xref="p1.1.m1.1.7">fragments</csymbol>
          <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">(</ci>
          <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">ln</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">ρ</csymbol>
          <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20"></ci>
        </cerror>
        <eq id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
        <minus id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22"/>
        <csymbol cd="unknown" id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">k</csymbol>
        <apply id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">
          <csymbol cd="ambiguous" id="p1.1.m1.1.32.1.cmml" xref="p1.1.m1.1.32">subscript</csymbol>
          <sum id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24"/>
          <ci id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">𝛼</ci>
        </apply>
        <apply id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">
          <csymbol cd="ambiguous" id="p1.1.m1.1.33.1.cmml" xref="p1.1.m1.1.33">subscript</csymbol>
          <ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">𝑝</ci>
          <ci id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27.1">𝛼</ci>
        </apply>
        <ci id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">ln</ci>
        <apply id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">
          <csymbol cd="ambiguous" id="p1.1.m1.1.34.1.cmml" xref="p1.1.m1.1.34">subscript</csymbol>
          <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">𝑝</ci>
          <ci id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">𝛼</ci>
        </apply>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle S:=-k\left\langle\operatorname{ln}\rho\right%
\rangle=-k\operatorname{Tr}\left(\operatorname{ln}\rho\right\rangle=-k\sum_{%
\alpha}p_{\alpha}\operatorname{ln}p_{\alpha}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (989 B / 307 B) :

S:=klnρ=kTr(lnρ=kαpαlnpα
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>S</mi><mi>:</mi><mo>=</mo><mo>&#x2212;</mo><mi>k</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi>ln</mi><mo>&#x2061;</mo><mi>&#x03C1;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><mo>&#x2212;</mo><mi>k</mi><mi data-mjx-texclass="OP" mathvariant="normal">Tr</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ln</mi><mo>&#x2061;</mo><mi>&#x03C1;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><mo>&#x2212;</mo><mi>k</mi><munder><mo texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></munder><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msub><mi>ln</mi><mo>&#x2061;</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msub></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Prüfungsfragen:Statistische Physik page

Identifiers

  • S
  • k
  • ρ
  • k
  • ρ
  • k
  • α
  • pα
  • pα

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results