论文标题
QCD物质的热力学特性和运输系数在非扩展的Polyakov-nambu-Jona-Lasinio模型中
Thermodynamic properties and transport coefficients of QCD matter within the non-extensive Polyakov-Nambu-Jona-Lasinio model
论文作者
论文摘要
我们提出了基于非扩展统计力学的Polyakov-Nambu-Jona-Lasinio模型的非扩展版本。该新统计数据的特征是无量纲的非扩张性参数$ Q $，该$ Q $ $ q $ t y违反了Boltzmann-Gibbs统计的假设（当$ Q \ rightArrow1 $时，它返回到Boltzmann-Gibbs案例）。使用此Q-Polyakov-nambu-Jona-lasinio模型，并包括两个不同的Polyakov-loop电位，我们讨论了参数$ Q $对手性和反登录相变的影响，各种热力学数量以及在有限的温度和零QUARK化学电位上的各种热力学数量和传输系数。我们发现Stefan-Boltzmann限制实际上与统计的选择有关。 For example, in the Tsallis statistics, the thermodynamic quantities $\fracε{T^{4}}$, $\frac{p}{T^{4}}$ and $\frac{s}{T^{3}}$ all increase with $q$, exceed their usual Stefan-Boltzmann limits and tend to a new $q$-related温度足够高的tsallis极限。但是，有趣的是，由于令人惊讶的取消，$ c_ {s}^{2} $的高温限制仍然是其SB限制$ 1/3 $。此外，我们发现了非扩展效应与有限尺寸效应之间的一些相似之处。例如，随着$ q $的增加（尺寸减小），$ \ frac {c_ {v}}} {t^{3}} $和$ c_ {s}^{2} $的关键性逐渐消失。此外，为了更好地研究非扩展效果，我们定义了一种新的敏感性，并计算了热力学数量和运输系数的响应，对$ q $。并发现它们的响应模式不同。
We present a non-extensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the non-extentive statistical mechanics. This new statistics is characterized by a dimensionless non-extensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when $q\rightarrow1$, it returns to the Boltzmann-Gibbs case). Using this q-Polyakov-Nambu-Jona-Lasinio model and including two different Polyakov-loop potentials, we discussed the influence of the parameter $q$ on chiral and deconfinement phase transition, various thermodynamic quantities and transport coefficients at finite temperature and zero quark chemical potential. We found that the Stefan-Boltzmann limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities $\fracε{T^{4}}$, $\frac{p}{T^{4}}$ and $\frac{s}{T^{3}}$ all increase with $q$, exceed their usual Stefan-Boltzmann limits and tend to a new $q$-related Tsallis limit at temperature high enough. Interestingly, however, due to a surprising cancellation, the high temperature limit of $c_{s}^{2}$ is still its SB limit $1/3$. In addition, we found some similarities between the non-extensive effect and the finite-size effect. For example, as $q$ increases (size decreases), the criticality of $\frac{c_{v}}{T^{3}}$ and $c_{s}^{2}$ gradually disappears. Besides, in order to better study the non-extensive effect, we defined a new susceptibility and calculated the response of thermodynamic quantities and transport coefficients to $q$. And found that their response patterns are different.
