https://vasp.at/wiki/index.php?action=history&feed=atom&title=Category%3AEnsemble_properties 2026-04-10T13:27:46Z Revision history for this page on the wiki MediaWiki 1.40.1 https://vasp.at/wiki/index.php?title=Category:Ensemble_properties&diff=16500&oldid=prev 2022-04-08T11:55:54Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:55, 8 April 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td> <td colspan="2" class="diff-lineno">Line 13:</td></tr> <tr><td class="diff-marker"></td><td style="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;"><div>== References ==</div></td><td class="diff-marker"></td><td style="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;"><div>== References ==</div></td></tr> <tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>[[<del style="font-weight: bold; text-decoration: none;">:</del>Category:VASP| Ensemble properties]][[Category:Molecular dynamics|Molecular dynamics]]</div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>[[Category:VASP| Ensemble properties]][[Category:Molecular dynamics|Molecular dynamics]]</div></td></tr> <!-- diff cache key mediawiki-vw:diff::1.12:old-16495:rev-16500 --> </table>

Huebsch https://vasp.at/wiki/index.php?title=Category:Ensemble_properties&diff=16495&oldid=prev 2022-04-08T11:48:21Z

<p>Huebsch moved page <a href="/wiki/Ensemble_properties" class="mw-redirect" title="Ensemble properties">Ensemble properties</a> to <a href="/wiki/Category:Ensemble_properties" title="Category:Ensemble properties">Category:Ensemble properties</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:48, 8 April 2022</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Huebsch https://vasp.at/wiki/index.php?title=Category:Ensemble_properties&diff=16494&oldid=prev 2022-04-08T11:48:04Z

<p>Created page with &quot;In a <a href="/wiki/Category:Molecular_dynamics" title="Category:Molecular dynamics">molecular-dynamics</a> calculation, VASP simulates a specific <a href="/wiki/Category:Ensembles" title="Category:Ensembles">ensemble</a>. In principle, any property of the system can...&quot;</p> <p><b>New page</b></p><div>In a [[:Category:Molecular dynamics|molecular-dynamics]] calculation, VASP simulates a specific [[:Category:Ensembles|ensemble]]. In principle, any property of the system can be monitored, and then one can take the ensemble average of this property. For some observables, VASP provides convenient tags, articles, and files that help evaluate these so-called &#039;&#039;&#039;ensemble properties&#039;&#039;&#039;.<br /> <br /> == Theory ==<br /> <br /> For any property &lt;math&gt;\mathcal{A}&lt;/math&gt; of the system, we can define the observable macroscopic property &lt;math&gt;\mathcal{A}_{\mathrm{obs}}&lt;/math&gt; by taking the ensemble average:<br /> ::&lt;math&gt;<br /> \mathcal{A}_{\mathrm{obs}} = \left\langle \mathcal{A}\left(p(t), q(t)\right)\right\rangle_{\mathrm{time}} = \lim_{t_{\mathrm{obs}} \to \infty} \frac{1}{t_{\mathrm{obs}}} \int_0^{t_{\mathrm{obs}}} \, \mathcal{A}\left(p(t), q(t)\right) \, \mathrm{d}t.<br /> &lt;/math&gt;<br /> Here, &lt;math&gt;t_\mathrm{obs}&lt;/math&gt; corresponds to the simulation time, &lt;math&gt;p(t)&lt;/math&gt; and &lt;math&gt;q(t)&lt;/math&gt; are the canonical momenta and positions, and an average of &lt;math&gt;\mathcal{A}\left(p(t), q(t)\right)&lt;/math&gt; is taken over time &lt;math&gt;t&lt;/math&gt;. <br /> <br /> == How to ==<br /> <br /> == References ==<br /> <br /> [[:Category:VASP| Ensemble properties]][[Category:Molecular dynamics|Molecular dynamics]]</div>

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