Caratheodory's formulation of the second law of thermodynamics describes states that are not accessible via paths with vanishing heat differential.
One quantity that is described as this kind of invariant is the magnetic moment of a charged particle as it gyrates around magnetic field lines; that invariant is an approximation to a Poincare invariant. One theorem of this name gives conditions under which a Hamiltonian will acquire a measurable geometric phase in a cyclic process. That theorem states that a Hamiltonian that is (*) perturbed in this manner will evolve into an eigenstate of the perturbed Hamiltonian. Caratheodory's formulation of the second law of thermodynamics describes states that are not accessible via paths with vanishing heat differential. An "index" of this name is equal to one, plus two divided by the number of degrees of freedom available to a molecule; that index is also the ratio of specific heats. For 10 points, give this term that describes thermodynamic processes that occur without heat transfer.
One quantity that is described as this kind of invariant is the magnetic moment of a charged particle as it gyrates around magnetic field lines; that invariant is an approximation to a Poincare invariant.
adiabatic [accept isentropic; accept adiabatic invariant or adiabatic theorem or adiabatic process or adiabatic index]