Chamberlin Ralph V
Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA.
Entropy (Basel). 2024 Feb 23;26(3):190. doi: 10.3390/e26030190.
The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any N, with dynamics that is readily altered from reversible to irreversible. We find thermal-equilibrium behavior in the thermodynamic limit, and in systems as small as N=2, but both results require microscopic dynamics that is intrinsically irreversible.
热力学第二定律导致熵不可逆地增加，直至达到热平衡。这种不可逆的增加通常被认为需要从可逆的微观物理定律中产生大型复杂系统。我们使用N个伊辛自旋的一维环与N个爱因斯坦振子的显式热库耦合的模拟和理论来检验这一假设。该系统的简单性使得对于任何N都能精确计算出自旋和热库的熵，其动力学很容易从可逆变为不可逆。我们在热力学极限以及小至N = 2的系统中发现了热平衡行为，但这两个结果都需要本质上不可逆的微观动力学。
