= Dissipative Liouville equation
{title2=$\partial_tP+\nabla_z\cdot(bP)=0$}
Conservation of <probability> under a deterministic <characteristic flow map> with <velocity> $b(z,t)$ gives the displayed <continuity equation> on <phase space>. Along a characteristic, $dP/dt=-P\nabla_z\cdot b$. Unlike the <Hamiltonian Liouville equation>, it allows contraction of phase-space volume and increasing density along trajectories. It still preserves total <probability> when boundary fluxes vanish.
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