McKean Entropy-Production Conjecture

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This event attributed to Claude

McKean Entropy-Production Conjecture parent of this event

This event attributed to Luis Silvestre

McKean Entropy-Production Conjecture evidence for this event

This event attributed to GPT-5.6 Sol

VibeMathed record: McKean Entropy-Production Conjecture evidence for this event

For the space-homogeneous Boltzmann equation in dimension $3$ with collision kernels $$B=\frac{1}{4\pi}|v-v_*|^\gamma,\qquad \gamma\in[0,1],$$ the paper constructs smooth, positive, radial mixtures $f_R=(1-p)M_1+pM_R$ for which $\partial_tD(f_R)>0$ for sufficiently large $R$. Thus entropy production need not decrease even for Maxwell molecules ($\gamma=0$) or hard spheres ($\gamma=1$), negatively resolving McKean's monotonicity question for these physically standard kernels. parent of this event