p17

Section 1.1  Being macroscopic---why do we need statistics?

Conceptual

1. *`Macroscopic,’ and `equilibrium’
   

2. *Partition/reconstruction invariance of thermodynamic observables
   

    We must pay due attention to the nature and characteristics of thermodynamic observables (esp., the zeroth and the fourth laws; however, without the first and the second laws we cannot really specify what a thermodynamic state is).

1. *Statistics in statistical mechanics does not describe the `true’ statistics of the states actually realized in a macroscopic equilibrium system.  Statistics is a `trick’ or `filter’ to extract thermodynamic observables from microscopic mechanical description of the system.
   

Technical

*Homogeneous functions and Euler’s theorem, Gibbs-Duhem relation

*Precise definition of ergodicity; it is a property of a measure-theoretical dynamical system.