论文标题
时间可逆的热力学不可逆性：一维热传导振荡器和二维牛顿冲击波
Time-Reversible Thermodynamic Irreversibility : One-Dimensional Heat-Conducting Oscillators and Two-Dimensional Newtonian Shockwaves
论文作者
论文摘要
我们分析了两种不可逆模拟类型的时间可逆力学。第一个是耗散的一维热传导振荡器，该振荡器在三维相空间中暴露于温度梯度，坐标$ q $，动量$ p $和恒温器控制变量$ζ$。第二种类型模拟了保守的二维$ n $ body-body-body-body变量$ \ {q，p \} $接受冲击压缩。尽管三个振荡器方程中的每个振荡器方程和所有4n $运动方程的所有类型的仿真都不可逆，但所有$ 4N $ 4N $ 4N $ 4N $ 4N $的时间可逆，遵守了热力学的第二定律。但是出于不同的原因。不可逆的振荡器寻求有吸引力的耗散限制周期。牛顿冲击波同样是不可逆转但完全保守的，最终产生了可逆的近平衡型稀疏迷。两种问题类型都说明了Lyapunov不稳定性的有趣特征。
We analyze the time-reversible mechanics of two irreversible simulation types. The first is a dissipative one-dimensional heat-conducting oscillator exposed to a temperature gradient in a three-dimensional phase space with coordinate $q$, momentum $p$, and thermostat control variable $ζ$. The second type simulates a conservative two-dimensional $N$-body fluid with $4N$ phase variables $\{q,p\}$ undergoing shock compression. Despite the time-reversibility of each of the three oscillator equations and all of the $4N$ manybody motion equations both types of simulation are irreversible, obeying the Second Law of Thermodynamics. But for different reasons. The irreversible oscillator seeks out an attractive dissipative limit cycle. The likewise irreversible, but thoroughly conservative, Newtonian shockwave eventually generates a reversible near-equilibrium pair of rarefaction fans. Both problem types illustrate interesting features of Lyapunov instability.
