The quench dynamics of many-body quantum systems may exhibit nonanalyticities in the Loschmidt echo, a phenomenon known as dynamical phase transition (DPT). Despite considerable research into the underlying mechanisms behind this phenomenon, several open questions still remain. Motivated by this, we put forth a detailed study of DPTs from the perspective of quantum phase space and entropy production, a key concept in thermodynamics. We focus on the Lipkin-Meshkov-Glick model and use spin-coherent states to construct the corresponding Husimi-$Q$ quasiprobability distribution. The entropy of the $Q$ function, known as Wehrl entropy, provides a measure of the coarse-grained dynamics of the system and, therefore, evolves nontrivially even for closed systems. We show that critical quenches lead to a quasimonotonic growth of the Wehrl entropy in time, combined with small oscillations. The former reflects the information scrambling characteristic of these transitions and serves as a measure of entropy production. On the other hand, the small oscillations imply negative entropy production rates and therefore signal the recurrences of the Loschmidt echo. Finally, we also study a Gaussification of the model based on a modified Holstein-Primakoff approximation. This allows us to identify the relative contribution of the low-energy sector to the emergence of DPTs. The results presented in this article are relevant not only from the dynamical quantum phase transition perspective but also for the field of quantum thermodynamics, since they point out that the Wehrl entropy can be used as a viable measure of entropy production.

中文翻译：

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动态量子相变中的韦尔熵生产率

多体量子系统的猝灭动力学可能在Loschmidt回波中表现出非解析性，这种现象称为动态相变（DPT）。尽管对这种现象背后的潜在机制进行了大量研究，但仍然存在一些悬而未决的问题。因此，我们从量子相空间和熵产生（热力学中的关键概念）的角度对DPT进行了详细的研究。我们专注于Lipkin-Meshkov-Glick模型，并使用自旋相干态构造相应的Husimi-$问$准概率分布。的熵$问$称为Wehrl熵的函数提供了系统粗粒度动态的度量，因此，即使对于封闭系统，它也可以平凡地演化。我们显示临界淬灭导致Wehrl熵在时间上准拟音速增长，并伴有小振荡。前者反映了这些转变的信息加扰特征，并作为熵产生的量度。另一方面，小的振荡意味着负的熵产生速率，因此表明了Loschmidt回波的重复出现。最后，我们还研究了基于修正的Holstein-Primakoff逼近的模型的高斯化。这使我们能够确定低能耗行业对DPT的出现的相对贡献。