Equilibrium

  1. Based on a system's independent variables, the concept of equilibrium can be divided into three categories: isolated systems, systems in contact with a reservoir of constant temperature, and systems in contact with a reservoir of constant temperature and pressure [Rei, §8.1, §8.2 and §8.3].

    1. Common misconceptions about equilibrium. Let v1 be the number of particles going from the system to the reservoir per unit time and v2 be the number of particles going from the reservoir to the system per unit time.

      1. Misconception #1. When v1=v2, the system and the reservoir are in equilibrium.
        Why is the above statement incorrect?
        Equilibrium must be described in terms of states.

      2. Misconception #2. When the system and the reservoir are in equilibrium, v1=v2.
        Why is the above statement incorrect?
        Like an eigenvalue in quantum mechanics, the measurement of a system's particle number is legitimate only if the state of the system is specified. The net rate v1=v2 depends on the system's initial state and final state during the measurement.
        Correct statement: Most probably (the sample space is the state space of the system), v1=v2. However, there is a tiny probability that v1>>v2 and also a tiny probability that v2>>v1.

      3. Misconception #3. When an isolated system is in equilibrium, the particle number of each chemical species in the system is fixed.
        Similiar to (ii), the correct statement should be as follows:
        Most probably, the particle number of each chemical species in the system is fixed. However, there is a tiny probability that the particle number of a certain chemical species in the system changes significantly.

    2. To derive [Kit, p.267, (30)], Kittel establishes dG=0 [Kit, p.266, l.−1] first. However, Kittel bases on his argument on Misconception #3 to prove dG=0, see [Kit, p.262, l.−2]. At best, all Kittel can conclude is that most probably, dG=0. For a correct proof of dG=0, see [Rei, p.296, (8.3.6)].


  2. The contrast between an isolated system and a system in a reservoir is not limited to thermodynamics. It can be applied to electrostatics also [Wangs, p.104, l.10-p.106, l.-10].