论文标题
统计物理学中的量子和经典方法：一些基本不平等现象
Quantum and classical approaches in statistical physics: some basic inequalities
论文作者
论文摘要
我们提出了自由能，熵和平均能量的经典和量子值之间的一些基本不平等。我们研究了从确定性案例（经典力学）到概率案例（量子力学）的过渡。在本文的第一部分中，我们假设降低的普朗克常数$ \ hbar $，绝对温度$ t $，振荡器$ω$的频率以及系统$ n $的自由度是固定的。比较量子和经典力学问题的方法是新的（请参阅[35] - [37]）。 在本文的第二部分中，我们同时得出了四种情况的半经典限制，也就是说，对于$ \ hbar {\ to} 0 $，$ t {\ to} \ to} \ infty $，$ω{\ to} 0 $，和$ n {\ to} {\ to} \ infty $。我们注意到，通常在量子力学中考虑了$ \ hbar {\ to} 0 $的情况（请参阅[21]）。 M. Planck和A. Einstein最初研究了$ t {\ to} \ infty $和$ω{\ to} 0 $的$ω{\ to} 0 $。
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum mechanics). In the first part of the paper, we assume that the reduced Planck constant $\hbar$, the absolute temperature $T$, the frequency of an oscillator $ω$, and the degree of freedom of a system $N$ are fixed. This approach to the problem of comparing quantum and classical mechanics is new (see [35]--[37]). In the second part of the paper, we simultaneously derive the semiclassical limits for four cases, that is, for $\hbar{\to}0$, $T{\to}\infty$, $ω{\to}0$, and $N{\to}\infty$. We note that only the case $\hbar{\to}0$ is usually considered in quantum mechanics (see [21]). The cases $T{\to}\infty$ and $ω{\to}0$ in quantum mechanics were initially studied by M. Planck and by A. Einstein, respectively.
