When does a Boltzmannian equilibrium exist?
Werndl, C. & Frigg, R.
(2023).
When does a Boltzmannian equilibrium exist?
In
Soto, C.
(Ed.),
Current Debates in Philosophy of Science: In Honor of Roberto Torretti
(pp. 247 – 273).
Springer Nature Switzerland.
https://doi.org/10.1007/978-3-031-32375-1_10
(2023).
When does a Boltzmannian equilibrium exist?
In
Soto, C.
(Ed.),
Current Debates in Philosophy of Science: In Honor of Roberto Torretti
(pp. 247 – 273).
Springer Nature Switzerland.
https://doi.org/10.1007/978-3-031-32375-1_10
We present a definition of equilibrium for Boltzmannian statistical mechanics based on the long-run fraction of time a system spends in a state. We then formulate and prove an existence theorem which provides general criteria for the existence of an equilibrium state. We illustrate how the theorem works with toy example. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas.