Why are momentum and angular momentum not state quantities in thermodynamics? I am recently studying thermodynamics and was wondering if energy is a state quantity, why aren't momentum and angular momentum? I feel like they are always zero at equilibrium in ideal gas based on Maxwell-Boltzman distribution. Is this general for all system in equilibrium? Thanks!
 A: Total momentum and angular momentum, in the cases they are constant of motion, are state varibles, as well as total energy or volume.
From the physical point of view it is quite clear that the state of the whole system may require to specify momentum or angular momentum.
From a more theoretical point of view, any independent constant of motion introduces a partition of the phase space into separate ergodic components, each component being characterized by a set of values of the constants of motion.
In the early stages of computer simulation of fluid system, it took  some time before people realized that in order to compare properly molecular dynamics (MD) and Monte Carlo (MC) simulations, one has to take into account   that the simplest implementation of such two computer simulation methods corresponds to two different ensembles: conserving total momentum, in the case of MD, or non-conserving total momentum (the usual canonical ensemble, at the base of MC simulation). The MD ensemble differs from the microcanonical ensemble just because total momentum is fixed as well as the total energy.
In the volume on Statistical Mechanics of Landau Lifshitz's textbook, it is possible to find a discussion of thermodynamics in a rotating system frame, directly connected to this question.
