Abe Sumiyoshi
Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, People's Republic of China.
Institute of Physics, Kazan Federal University, Kazan 420008, Russia.
Philos Trans A Math Phys Eng Sci. 2020 May;378(2170):20190196. doi: 10.1098/rsta.2019.0196. Epub 2020 Mar 30.
In non-equilibrium classical thermostatistics, the state of a system may be described by not only dynamical/thermodynamical variables but also a kinetic distribution function. This 'double structure' bears some analogy with that in quantum thermodynamics, where both dynamical variables and the Hilbert space are involved. Recently, the concept of weak invariants has repeatedly been discussed in the context of quantum thermodynamics. A weak invariant is defined in such a way that its value changes in time but its expectation value is conserved under time evolution prescribed by a kinetic equation. Here, a new aspect of a weak invariant is revealed for the classical Fokker-Planck equation as an example of classical kinetic equations. The auxiliary field formalism is applied to the construction of the action for the kinetic equation. Then, it is shown that the auxiliary field is a weak invariant and is the Noether charge. The action is invariant under the transformation generated by the weak invariant. The result may shed light on possible roles of the symmetry principle in the kinetic descriptions of non-equilibrium systems. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
在非平衡经典统计热力学中，系统的状态不仅可以用动力学/热力学变量来描述，还可以用动力学分布函数来描述。这种“双重结构”与量子热力学中的情况有一些相似之处，在量子热力学中，动力学变量和希尔伯特空间都被涉及。最近，弱不变量的概念在量子热力学的背景下被反复讨论。弱不变量的定义方式是，其值随时间变化，但其期望值在由动力学方程规定的时间演化下是守恒的。这里，以经典福克 - 普朗克方程作为经典动力学方程的一个例子，揭示了弱不变量的一个新方面。辅助场形式主义被应用于构建动力学方程的作用量。然后，表明辅助场是一个弱不变量且是诺特定荷。作用量在由弱不变量生成的变换下是不变的。该结果可能会揭示对称原理在非平衡系统动力学描述中的可能作用。本文是“非平衡热力学的基本方面”主题特刊的一部分。
