9 problems

Cercignani's conjecture. The entropy production term of the Boltzmann equation should be controlled by the relative entropy between $f$ and $\mathcal{M}_0(f)$ through an entropy-en…

Entropy–entropy production conjecture. There exists $\lambda_{\gamma,b}>0$ such that

Let a nonequilibrium steady state (NESS) on a dense network have entropy production rate $\sigma_{\mathrm{NESS}}$, and let … be the minimal entropy production over probability dist…

Generic nonexistence conjecture. Entropy-rate-admissible weak solutions possibly do not exist for a generic set of initial data.

Entropy-production conjecture. The conclusion of Theorem $$ should hold for every

Let $H(t)$ denote the entropy along a solution of the space-homogeneous Boltzmann equation. McKean's conjecture. McKean's first conjecture asserts that … This paper disproves the c…

Non-PMP and non-weak-Gibbs conjecture. For all $\Delta\in{\cal I}$, the unraveling $\mathbb{P}$ is not PMP and is not weak Gibbs.

Let $\Gamma_{N}$ denote the entropy production for symmetric probability densities $\psi_N$ on $\mathbb{S}^{N-1}(\sqrt{N})$, defined by … where the infimum is over all such probabi…

Villani's entropy-production conjecture. The bounds are essentially sharp, in the sense that