Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
Phys Rev E. 2017 Dec;96(6-1):062148. doi: 10.1103/PhysRevE.96.062148. Epub 2017 Dec 28.
Bridging the second law of thermodynamics and microscopic reversible dynamics has been a longstanding problem in statistical physics. Here, we address this problem on the basis of quantum many-body physics, and discuss how the entropy production saturates in isolated quantum systems under unitary dynamics. First, we rigorously prove that the entropy production does indeed saturate in the long time regime, even when the total system is in a pure state. Second, we discuss the non-negativity of the entropy production at saturation, implying the second law of thermodynamics. This is based on the eigenstate thermalization hypothesis, which states that even a single energy eigenstate is thermal. We also numerically demonstrate that the entropy production saturates at a non-negative value even when the initial state of a heat bath is a single energy eigenstate. Our results reveal fundamental properties of the entropy production in isolated quantum systems at late times.
将热力学第二定律与微观可逆动力学联系起来，一直是统计物理学中的一个长期存在的问题。在这里，我们基于量子多体物理学来解决这个问题，并讨论在幺正动力学下，孤立量子系统中的熵产生如何达到饱和。首先，我们严格证明了即使在总系统处于纯态的情况下，熵产生在长时间内确实会达到饱和。其次，我们讨论了在饱和时熵产生的非负性，这意味着热力学第二定律。这是基于本征态热化假设，该假设指出即使是单个能量本征态也是热的。我们还通过数值演示证明了，即使热浴的初始态是单个能量本征态，熵产生也会达到一个非负的饱和值。我们的结果揭示了孤立量子系统中熵产生在后期的基本性质。
