McCaul Gerard, Pechen Alexander, Bondar Denys I
Tulane University, New Orleans, Louisiana 70118, USA.
King's College London, London WC2R 2LS, United Kingdom.
Phys Rev E. 2019 Jun;99(6-1):062121. doi: 10.1103/PhysRevE.99.062121.
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new dynamical phase associated with such a construction is identified. By choosing distributions not belonging to this class, we produce explicit examples of both free particles and harmonic systems evolving in a bounded phase-space in such a way that entropy is nonconserved. While these nonconserving states are classically forbidden, they may be interpreted as states of a quantum system tunneling through a potential barrier boundary. In this case, the allowed boundary conditions are the only distinction between classical and quantum systems. We show that the boundary conditions for a tunneling quantum system become the criteria for entropy preservation in the classical limit. These findings highlight how boundary effects drastically change the nature of a system.
将厄米算符的自伴扩张理论应用于库普曼 - 冯·诺依曼经典力学，找到了哈密顿演化守恒熵的最一般概率分布集。识别出与这种构造相关的一个新的动力学相。通过选择不属于此类的分布，我们给出了自由粒子和谐振子系统在有界相空间中演化时熵不守恒的明确例子。虽然这些不守恒态在经典情况下是被禁止的，但它们可以被解释为量子系统隧穿势垒边界的态。在这种情况下，允许的边界条件是经典和量子系统之间的唯一区别。我们表明，隧穿量子系统的边界条件成为经典极限下熵守恒的标准。这些发现突出了边界效应如何极大地改变系统的性质。
