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==Prigogine's proposed theorem of minimum entropy production for very slow purely diffusive transfer==

==Prigogine's proposed theorem of minimum entropy production for very slow purely diffusive transfer==

In 1945 Prigogine (see also Prigogine (1947)) proposed a “Theorem of Minimum Entropy Production” which applies only to the purely diffusive linear regime, with negligible inertial terms, near a stationary thermodynamically non-equilibrium state. Prigogine's proposal is that the rate of entropy production is locally minimum at every point. The proof offered by Prigogine is open to serious criticism. A critical and unsupportive discussion of Prigogine's proposal is offered by Grandy (2008). It has been shown by Barbera that the total whole body entropy production cannot be minimum, but this paper did not consider the pointwise minimum proposal of Prigogine. A proposal closely related to Prigogine's is that the pointwise rate of entropy production should have its maximum value minimized at the steady state. This is compatible, but not identical, with the Prigogine proposal. Moreover, N. W. Tschoegl proposes a proof, perhaps more physically motivated than Prigogine's, that would if valid support the conclusion of Helmholtz and of Prigogine, that under these restricted conditions, the entropy production is at a pointwise minimum.

In 1945 Prigogine (see also Prigogine (1947)) proposed a “Theorem of Minimum Entropy Production” which applies only to the purely diffusive linear regime, with negligible inertial terms, near a stationary thermodynamically non-equilibrium state. Prigogine's proposal is that the rate of entropy production is locally minimum at every point. The proof offered by Prigogine is open to serious criticism. A critical and unsupportive discussion of Prigogine's proposal is offered by Grandy (2008). It has been shown by Barbera that the total whole body entropy production cannot be minimum, but this paper did not consider the pointwise minimum proposal of Prigogine. A proposal closely related to Prigogine's is that the pointwise rate of entropy production should have its maximum value minimized at the steady state. This is compatible, but not identical, with the Prigogine proposal. Moreover, N. W. Tschoegl proposes a proof, perhaps more physically motivated than Prigogine's, that would if valid support the conclusion of Helmholtz and of Prigogine, that under these restricted conditions, the entropy production is at a pointwise minimum.

1945年Prigogine(另见Prigogine(1947))提出了 "最小熵产生定理"，该定理只适用于静止的热力学非平衡状态附近的纯扩散线性体系，惯性项可忽略不计。Prigogine提出的是熵的产生速率在每一点上都是局部最小的。Prigogine提出的证明受到了严重的批评。Grandy(2008)对Prigogine的提议进行了批判性的和不支持的讨论。Barbera已经证明了全身熵产不能最小，但本文没有考虑Prigogine的点最小建议。与Prigogine的提议密切相关的是，熵产生的点率在稳态时应该有其最大值最小化。这与Prigogine的建议是一致的，但不完全相同。此外，N.W.Tschoegl提出了一个证明，也许比Prigogine的证明更有物理动机，如果有效的话，它将支持Helmholtz和Prigogine的结论，即在这些限制条件下，熵的产生是在一个点上最小的。

1945年Prigogine(另见Prigogine(1947))提出了 "最小熵产生定理"，该定理只适用于静止的热力学非平衡状态附近的纯扩散线性体系，惯性项可忽略不计。Prigogine提出的是熵的产生速率在每一点上都是局部最小的。Prigogine提出的证明受到了严重的批评。Grandy(2008)对Prigogine的提议进行了批判性的和不支持的讨论。Barbera已经证明了全身熵产不能最小，但本文没有考虑Prigogine的点最小建议。与Prigogine的提议密切相关的是，熵产生的点率在稳态时应该有其最大值最小化。这与Prigogine的建议是一致的，但不完全相同。此外，N.W.Tschoegl提出了一个证明，也许比Prigogine的证明更有物理动机，如果有效的话，它将支持Helmholtz和Prigogine的结论，即在这些限制条件下，熵的产生是在一个点上最小的。

== Faster transfer with convective circulation: second entropy ==

== Faster transfer with convective circulation: second entropy ==