在Srednicki的著名論文中提出，一個互相耦合的振子，其中單粒子的縮減密度矩陣會是熱態，其能階由量子力學中諧振子的能階所描述，且機率分布由波茲曼分布決定。換句話說，可以在不加入任何統計力學假設下得到一個相當於「溫度」的量。本論文想探討這個溫度（將其稱作量子溫度）是否有物理意義，方法是給出一個可解的多粒子耦合振盪模型，並期待在古典力學中也能得到一個對應的溫度。在古典力學中，我們在每顆粒子的初始條件引入一些隨機性，這種半古典的技巧使運動方程式接近朗之萬方程式，讓我們順利得到對應的溫度（將其稱作古典溫度）。比較結果顯示，量子溫度與由朗之萬方程式導出的古典溫度在函數形式上具有相似的行為。當兩溫度以耦合震盪的彈性常數為函數時，接存在一個極小值，而在那個極小值附近，兩者的溫度比值幾乎維持不變，變化小於 2%。

As shown by Srednicki \cite{Srednicki:1993im} that in the system of two simple harmonic oscillators coupled to each other, the reduced density matrix for a single particle is a thermal state. The energy spectrum is identical to that of a quantum harmonic oscillator in a thermal bath and follows the Boltzmann distribution. In other words, a quantity equivalent to a temperature emerges without introducing any assumptions from statistical mechanics. This thesis aims to investigate whether this temperature—referred to as the quantum temperature—has any physical meaning. To this end, an exactly solvable multi-particle coupled oscillator model is considered, with the hope of identifying a corresponding temperature in both the classical and quantum regime. In the classical framework, stochastic elements are introduced as the initial condition, forming a semi-classical approach that brings the dynamics close to the Langevin equation. This allows the identification of a corresponding temperature, here referred to as the classical temperature. The comparison shows that the quantum temperature and the classical temperature derived from the Langevin equation exhibit similar functional behavior. When both temperatures are considered as functions of the coupling spring constant, a local minimum appears. Near this minimum, the ratio between the two temperatures remains nearly constant, with variations less than 2%.