On the minimization of quantum entropies under local constraints
On the minimization of quantum entropies under local constraints
复制标题
局域约束下量子熵的最小化
DOI：
10.1016/j.matpur.2019.05.001
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Csu
中科院分区：
文献类型：
--
作者：
Romain Duboscq;Olivier Pinaud Imt;Csu
这项工作涉及在密度、电流和能量的局域约束下量子熵的最小化。这个问题出现在Degond和Ringhofer关于从第一原理推导量子流体动力学模型的工作中，这是对动态论中遇到的通过熵最小化的矩闭合策略的量子设置的适应。主要的数学困难是缺乏恢复能量约束所需的紧凑性。我们通过一个涉及能量、温度和熵的单调性论证来绕过这个问题，该论证受到一些热力学考虑的启发。
This work is concerned with the minimization of quantum entropies under local constraints of density, current, and energy. The problem arises in the work of Degond and Ringhofer about the derivation of quantum hydrodynamical models from first principles, which is an adaptation to the quantum setting of the moment closure strategy by entropy minimization encountered in kinetic theory. The main mathematical difficulty is the lack of compactness needed to recover the energy constraint. We circumvent this issue by a monotonicity argument involving energy, temperature and entropy, that is inspired by some thermodynamical considerations.