= Negative heat capacity of a virialized gravitational system
{title2=$dE/d\Theta=-3Nk_B/2$}
An isolated Newtonian system in <virial equilibrium> has total <energy> $E=K+W=-K$. Along an equilibrium sequence at fixed particle number, define the kinetic <temperature> by $K=3Nk_B\Theta/2$. Its <heat capacity> is therefore negative, as displayed: losing total energy increases the kinetic temperature. A <collisionless stellar system> need not have a thermodynamic temperature; this is a kinetic-temperature statement unless thermal equilibrium is additionally specified. Boundary pressure and external confinement can change the energy relation.
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