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equation and establish a form of Virial theorem . Using a maximum entropy production principle (MEPP), we derive a set of relaxation equations towards statistical equilibrium. These relaxation equations can ...
]. It is then important to understand what features change or are missed in a model of continuous culture by treating the cell population as an homogeneous system. In this work we propose to apply the maximum entropy ...
will prove in Theorem 3.3 below that this maximizer is unique and depends continuously on $$\epsilon$$.) Theorem 1.1. Let $$ H $$ be a $$k$$-starlike graph with $$\ell\ge 2$$ edges. Let $$\epsilon \in (0,1 ...
of absence of Cartan subalgebras for free group factors using free entropy methods [94, Theorem 5.2]. Shortly thereafter Ge [28] and Ge and Popa [30] used this machinery to prove that free group factors ...
], as mentioned in the “Introduction”, to find the parameters h (m, g) and J(m, g) of the maximum entropy distribution Eq (3) having mean activities m and raw pairwise correlations g. Starting with some values ...
and the volume growth entropy . The first characterization ( Theorem A) is in the space of Riemannian metrics with Ricci curvature bounded below and generalizes a result of Ledrappier and Wang [23]. The second ...
for the Hessian comparison theorem . From now on, we normalize |$G$| suitably so that |$G=r^{2-n}$| on the Euclidean space |$M={\mathbb{R}}^n$|. We define a function |$b$| as follows, \begin{ equation *} b:=G^\frac{1 ...
in |${\mathcal{M}}_{\sigma }(\Sigma )$|. Let |$\mu \in{\mathcal{M}}_{\sigma }(\Sigma )$| and recall that the Kolmogorov–Sinai entropy of |$\mu$| and |$\sigma$| is $$\begin{ equation *} h (\mu):= h (\mu,\sigma ...
disparity, denoted by e† [5–9] and life table entropy , denoted by H [10, 11], defined as (1) where ω is the maximum life span, and e(x) and f(x) are the remaining life expectancy and deaths distribution ...
the celebrated H - theorem (Villani, 2002). Based on this principle from kinetic theory, mathematicians have intensively developed the entropy method for the study of the large time behaviour of different systems ...
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