Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium.
Proc Natl Acad Sci U S A. 1983 Jul;80(14):4590-4. doi: 10.1073/pnas.80.14.4590.
The second law of thermodynamics, for quantum systems, is formulated, on the microscopic level. As for classical systems, such a formulation is only possible when specific conditions are satisfied (continuous spectrum, nonvanishing of the collision operator, etc.). The unitary dynamical group can then be mapped into two contractive semigroups, reaching equilibrium either for t --> +infinity or for t --> -infinity. The second law appears as a symmetry-breaking selection principle, limiting the observables and density functions to the class that tends to thermodynamic equilibrium in the future (for t --> +infinity). The physical content of the dynamical structure is now displayed in terms of the appropriate semigroup, which is realized through a nonunitary transformation. The superposition principle of quantum mechanics has to be reconsidered as irreversible processes transform pure states into mixtures and unitary transformations are limited by the requirement that entropy remains invariant. In the semigroup representation, interacting fields lead to units that behave incoherently at equilibrium. Inversely, nonequilibrium constraints introduce correlations between these units.
热力学第二定律，对于量子系统，是在微观层面上进行表述的。对于经典系统，只有在满足特定条件（连续谱、碰撞算子非零等）时才能进行这种表述。然后，可以将幺正动力学群映射到两个收缩半群中，分别在 t --> +infinity 或 t --> -infinity 时达到平衡。第二定律表现为一种对称破缺选择原理，将可观测量和密度函数限制在未来趋于热力学平衡的类中（对于 t --> +infinity）。动力学结构的物理内容现在以适当的半群来表示，这是通过非幺正变换来实现的。量子力学的叠加原理必须重新考虑，因为不可逆过程将纯态转变为混合物，并且幺正变换受到熵保持不变的要求的限制。在半群表示中，相互作用的场导致在平衡时表现出不协调的单元。相反，非平衡约束在这些单元之间引入相关性。
