A unified approach to resolving the entropy production paradox
A unified approach to resolving the entropy production paradox
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DOI：
10.1515/jnetdy-2012-0008
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发表时间：
2012-12-01
影响因子：
6.6
通讯作者：
Prehl, Janett
中科院分区：
文献类型：
--
作者：
Hoffmann, Karl Heinz;Essex, Christopher;Prehl, Janett
通过使用基于时间或空间分数阶微分算子的分数阶扩散方程，可以将扩散和波传播的两个范式演化方程所代表的完全不可逆和完全可逆动力学之间的状态桥接起来。这些桥梁的特点是由一个单参数家庭的分布函数。在这两种情况下，我们都会遇到一个反直觉的行为：越接近可逆的情况，熵产生就越大。这个特征被称为熵产生悖论，并且可以部分地解决时间分数的情况下，通过使用分布平均值作为一种方式来表征过程的内部快速性，而对于空间分数的情况下，使用一个特殊的位置参数。在这里，我们能够提出一个统一的方法的基础上的分布模式作为适当的措施，内部的快速的过程。
Bridging the regime between fully irreversible and fully reversible dynamics as represented by the two paradigmatic evolution equations for diffusion and wave propagation became possible by the use of fractional diffusion equations based on time-or space-fractional differential operators. These bridges are each characterized by a one-parameter family of distribution functions. In both cases one encounters a counter-intuitive behavior: the closer one gets to the reversible case, the larger the entropy production becomes. This feature is known as the entropy production paradox, and could be partly resolved for the time-fractional case by using the distribution mean as a way to characterize the internal quickness of the process, while for the space-fractional case a special location parameter was used. Here we are able to present a unified approach based on the distribution modes as the appropriate measure for the internal quickness of the processes.