= Solution
\b[False as a claimed change between isolated steady endpoints.] <Conservation of energy> by itself would allow a more negative $W$ and a larger $T$, but both endpoints must also obey the <virial theorem>. For a finite isolated equilibrium with no surface term,
$$
2T+W=0,\qquad E=T+W=-T=\frac W2.
$$
If total $E$ is conserved between the two equilibria, the <fixed-energy virial constraint between steady states> gives
$$
\boxed{T_{\mathrm{final}}=T_{\mathrm{initial}}=-E,\qquad W_{\mathrm{final}}=W_{\mathrm{initial}}=2E.}
$$
This $T$ includes both ordered rotation and random stellar motion. A <galactic bar> or other instability can redistribute <angular momentum> and concentrate a central component, but compensating expansion or rearrangement elsewhere must preserve the global energy constraint. Central concentration alone does not prove that the whole system has a more negative $W$.
A remnant could have different energies if <stars> escape, or if an external component exchanges energy with it; then the conserved total energy would include that other component. Those cases do not justify treating the bound disc simultaneously as a closed fixed-energy system and as a new equilibrium with increased $T$.
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