论文标题
内部能量，基本热力学关系和吉布斯的整体理论作为统计计数定律
Internal Energy, Fundamental Thermodynamic Relation, and Gibbs' Ensemble Theory as Laws of Statistical Counting
论文作者
论文摘要
计数ad infinitum是在独立重复采样下具有有限状态的统计动力学可观察到的全息图。熵提供了观察到的频率$ \ hat {\boldsymbolν} $ W.R.T.的无限概率。概率先前$ {\ bf p} $。在Callen的假设和Legendre-Fenchel Transform之后，在没有机械的帮助下，我们显示了内部能量$ \BoldSymbolμ$；它提供了具有完整或部分信息的实用可观察到的线性表示。吉布斯的基本热力学关系和合奏理论在数学上遵循。 $ \boldsymbolμ$是$ \ hat {\boldsymbolν} $ $ω$在傅立叶分析中to $ t $。
Counting ad infinitum is the holographic observable to a statistical dynamics with finite states under independent repeated sampling. Entropy provides the infinitesimal probability for an observed frequency $\hat{\boldsymbolν}$ w.r.t. a probability prior ${\bf p}$. Following Callen's postulate and through Legendre-Fenchel transform, without help from mechanics, we show an internal energy $\boldsymbolμ$ emerges; it provides a linear representation of real-valued observables with full or partial information. Gibbs' fundamental thermodynamic relation and theory of ensembles follow mathematically. $\boldsymbolμ$ is to $\hat{\boldsymbolν}$ what $ω$ is to $t$ in Fourier analysis.
