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	<title>Particles vs Waves: Finite Topological Thermodynamics - Revision history</title>
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	<updated>2026-04-10T09:47:17Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://naturalphilosophy.org/wiki/index.php?title=Particles_vs_Waves:_Finite_Topological_Thermodynamics&amp;diff=24709&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="http://naturalphilosophy.org/wiki/index.php?title=Particles_vs_Waves:_Finite_Topological_Thermodynamics&amp;diff=24709&amp;oldid=prev"/>
		<updated>2017-01-02T02:49:15Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 22:49, 1 January 2017&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot;&gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper|particles vs waves finite topological thermodynamics]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper|particles vs waves finite topological thermodynamics]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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		<author><name>Maintenance script</name></author>
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	<entry>
		<id>http://naturalphilosophy.org/wiki/index.php?title=Particles_vs_Waves:_Finite_Topological_Thermodynamics&amp;diff=19874&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="http://naturalphilosophy.org/wiki/index.php?title=Particles_vs_Waves:_Finite_Topological_Thermodynamics&amp;diff=19874&amp;oldid=prev"/>
		<updated>2017-01-01T17:52:49Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 13:52, 1 January 2017&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l12&quot;&gt;Line 12:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 12:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Traditional physical theories have been constrained historically by assumptions of &quot;geo-metrical&quot; di?eomorphisms, invariant symmetries, and topological invariance. These ideas are useful to the understanding of equilibrium thermodynamic states, and processes that lead to time reversibility of equilibrium topological systems, and the conservation of energy. However, the geometrical constraints o?er no insight into non-equilibrium thermodynamic systems and irreversible processes, such as observed in the biological environment. Geometrical tensor methods are inadequate and must be replaced by topological thinking. Emphasis must be placed upon methods that describe continuous topological evolution, and not topological invariance. For example, to form a categorical marriage between gravity and quantum mechanics requires the recognition that the topological structure of &quot;particles&quot; is di?erent from the topological structure of &quot;waves&quot;.[[Category:Scientific Paper]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Traditional physical theories have been constrained historically by assumptions of &quot;geo-metrical&quot; di?eomorphisms, invariant symmetries, and topological invariance. These ideas are useful to the understanding of equilibrium thermodynamic states, and processes that lead to time reversibility of equilibrium topological systems, and the conservation of energy. However, the geometrical constraints o?er no insight into non-equilibrium thermodynamic systems and irreversible processes, such as observed in the biological environment. Geometrical tensor methods are inadequate and must be replaced by topological thinking. Emphasis must be placed upon methods that describe continuous topological evolution, and not topological invariance. For example, to form a categorical marriage between gravity and quantum mechanics requires the recognition that the topological structure of &quot;particles&quot; is di?erent from the topological structure of &quot;waves&quot;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Scientific Paper&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|particles vs waves finite topological thermodynamics&lt;/ins&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Gravity]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category:Gravity]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Maintenance script</name></author>
	</entry>
	<entry>
		<id>http://naturalphilosophy.org/wiki/index.php?title=Particles_vs_Waves:_Finite_Topological_Thermodynamics&amp;diff=7530&amp;oldid=prev</id>
		<title>Maintenance script: Imported from text file</title>
		<link rel="alternate" type="text/html" href="http://naturalphilosophy.org/wiki/index.php?title=Particles_vs_Waves:_Finite_Topological_Thermodynamics&amp;diff=7530&amp;oldid=prev"/>
		<updated>2016-12-30T16:41:07Z</updated>

		<summary type="html">&lt;p&gt;Imported from text file&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Infobox paper&lt;br /&gt;
| title = Particles vs Waves: Finite Topological Thermodynamics&lt;br /&gt;
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_6820.pdf Link to paper]&lt;br /&gt;
| author = [[Robert M Kiehn]]&lt;br /&gt;
| published = 2012&lt;br /&gt;
| journal = [[None]]&lt;br /&gt;
| num_pages = 22&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Read the full paper&amp;#039;&amp;#039;&amp;#039; [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_6820.pdf here]&lt;br /&gt;
&lt;br /&gt;
==Abstract==&lt;br /&gt;
&lt;br /&gt;
Traditional physical theories have been constrained historically by assumptions of &amp;quot;geo-metrical&amp;quot; di?eomorphisms, invariant symmetries, and topological invariance. These ideas are useful to the understanding of equilibrium thermodynamic states, and processes that lead to time reversibility of equilibrium topological systems, and the conservation of energy. However, the geometrical constraints o?er no insight into non-equilibrium thermodynamic systems and irreversible processes, such as observed in the biological environment. Geometrical tensor methods are inadequate and must be replaced by topological thinking. Emphasis must be placed upon methods that describe continuous topological evolution, and not topological invariance. For example, to form a categorical marriage between gravity and quantum mechanics requires the recognition that the topological structure of &amp;quot;particles&amp;quot; is di?erent from the topological structure of &amp;quot;waves&amp;quot;.[[Category:Scientific Paper]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Gravity]]&lt;/div&gt;</summary>
		<author><name>Maintenance script</name></author>
	</entry>
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