Observation of a Persistent Non-Equilibrium State in an Extremely Isotropic Harmonic Potential

<p>Ludwig Boltzmann made tremendously important contributions to the problem of connecting\&nbsp;<span style="line-height: 1.6em;">macroscopic, empirical phenomena with microscopic, atomistic dynamics. At the end\&nbsp;</span><span style="line-height: 1.6em;">of the nineteenth century, Boltzmann was confronted with various strong objections to his\&nbsp;</span><span style="line-height: 1.6em;">work. For example, Boltzmann\textquoterights atomistic explanations presuppose the reality of atoms, a\&nbsp;</span><span style="line-height: 1.6em;">notion that was vigorously rejected in some circles [14, 38]. Then too, there was the critique\&nbsp;</span><span style="line-height: 1.6em;">by Loschmidt that Boltzmann\textquoterights H-theorem, put forth as a microscopic explanation for the\&nbsp;</span><span style="line-height: 1.6em;">Second Law of Thermodynamics, could hardly account for irreversible physics when the individual\&nbsp;</span><span style="line-height: 1.6em;">two-atom collisions were each reversible [18, 42]. Still intriguing today is the existence\&nbsp;</span><span style="line-height: 1.6em;">of special cases of the Boltzmann equation in which time-varying distributions of atoms resist\&nbsp;</span><span style="line-height: 1.6em;">the imperative of equilibration, even in the presence of collisions. Boltzmann discussed\&nbsp;</span><span style="line-height: 1.6em;">such situations in a paper dedicated to responding to Loschmidt\textquoterights critique [7, 4]. Perhaps\&nbsp;</span><span style="line-height: 1.6em;">Boltzmann\textquoterights motivation was to enumerate special cases where his famous H value does not\&nbsp;</span><span style="line-height: 1.6em;">relax as it should, and by enumerating them, point out their nonnaturalness, their artificiality.\&nbsp;</span><span style="line-height: 1.6em;">Damping, or relaxation to equilibrium, of a time-invariant phase-space distribution, is\&nbsp;</span><span style="line-height: 1.6em;">an all-but universal result predicted by the Boltzmann equation.</span></p>
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Ph. D.
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University of Colorado Boulder
Boulder, CO
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