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首页> 外文会议>Bayesian Inference and Maximum Entropy Methods in Science and Engineering >The Structure of Divergence(s) in Stationary State of Irreversible Heat Conduction Processes and their Partial Differential Equations of Elliptic Type
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The Structure of Divergence(s) in Stationary State of Irreversible Heat Conduction Processes and their Partial Differential Equations of Elliptic Type

机译：椭圆型不可逆热过程的稳态散度结构及其偏微分方程

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Irreversible processes mean entropy production or simply energy dissipation. This is true for stationary states too. The Laplace's equation for heat conduction as an elliptic linear second order partial differential equation does not express any energy dissipation in the conservative potential field according to the minimum principles. A new quasilinear elliptic type second order partial differential equation to stationary state heat conduction process was analyzed with the aid of minimum principles (and also on the base of the divergence term). Investigations made for Onsager and Prigogine principles showed the deciding role of local dissipation potentials. The existence of these potentials is basically a crucial point for real processes. The new quasilinear elliptic type partial differential equation of second order is in total agreement with Gyarmati's integral principle for stationary state too. Treating the above questions the proper Lagrange densities and the Euler-Lagrange differential equations must be applied in the different representational pictures (to treat the variational problems). On the base of the new equation(s) the different non-equilibrium temperatures can be determined for steady state irreversible processes but it cannot be done for the Laplace's equation. The structure of the divergence shows all these features. And what is more important one can find a connecting equation between the internal energy and the entropy (entropy production!) considering the steady state irreversible process. The new equation(s) interprets in a special way the results of the so-called dimensional analysis for nonlinear heat conduction in stationary state too. Boundary conditions were also taken into consideration. Discussion with heat reservoirs helps to expose the questions on the classical thermodynamic level too.
机译：不可逆过程意味着产生熵或仅仅是能量消耗。对于固定状态也是如此。根据最小原理，作为椭圆线性二阶偏微分方程的热传导拉普拉斯方程不表示保守势场中的任何能量耗散。借助于最小原理（以及在发散项的基础上），分析了一个新的拟线性椭圆型二阶偏微分方程到稳态热传导过程。对Onsager和Prigogine原理的研究表明了局部耗散潜力的决定性作用。这些潜力的存在基本上是实际过程的关键点。新的拟线性椭圆型二阶偏微分方程也完全符合Gyarmati稳态的积分原理。处理上述问题时，必须在不同的表示图片中应用适当的Lagrange密度和Euler-Lagrange微分方程（以处理变分问题）。在新方程式的基础上，可以为稳态不可逆过程确定不同的非平衡温度，但对于拉普拉斯方程式则无法做到。分歧的结构显示了所有这些特征。考虑到稳态不可逆过程，更重要的是可以找到内部能量与熵（熵产生！）之间的联系方程。新的方程式也以一种特殊的方式解释了稳态下非线性热传导的所谓尺寸分析的结果。边界条件也被考虑在内。与储热器的讨论也有助于在经典热力学水平上揭示问题。

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