= Isentropic decompression of a spherical linear trap
{title2=$T\propto a^{2/3}$}
At fixed atom number, the <entropy> of the <classical ideal gas in a spherical linear trap> depends on temperature and strength through $Z_1\propto T^{9/2}a^{-3}$. Reversible adiabatic change therefore holds this product constant, giving the displayed relation. Reducing trap strength lowers the temperature while increasing cloud size. Its peak classical phase-space occupation $N/Z_1$ remains constant, so this cooling alone does not make the gas more quantum degenerate. Heat exchange, particle loss or irreversible entropy production would change this relation.
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