Adiabatic invariance

__Adiabatic invariants as effective Hamiltonians__

P. M. Bellan and R. J. Perkins, *Orbit-averaged quantities, the classical Hellmann-Feynman theorem,
and the magnetic flux enclosed by gyro-motion,* Phys.
Plasmas 22, 022108 (2015)

R. J. Perkins and P. M. Bellan, * Wheels within Wheels: Hamiltonian Dynamics as
a Hierarchy of Action Variables*, Phys.
Rev. Lett. 105, art 124301 (2010)

__Adiabatic invariants and the ideal gas law__

The conventional derivation of the ideal gas adiabatic law

* PV*^{gamma
}= constant

involves complex, non-intuitive arguments based on differences between specific heats at constant volume and constant pressure.

A new, intuitive derivation has been developed, based on the behavior of a particle bouncing elastically between two approaching walls. This derivation is in:

- P. M. Bellan, A microscopic, mechanical derivation of the adiabatic gas relation,
*American J. Phys.***72**, 679 (2004).

The derivation should be useful for a freshman physics class.