we will model the spaceship as an idealized box with perfectly reflecting walls. This is necessary, because the second law of thermodynamics applies only to thermally isolated systems, to which we can assign a Hamiltonian [5, section 11] [Landau L and Lifshitz E 1980 Statistical Physics vol 5, 3 edn (Pergamon)].
Among the various kinds of external interactions to which a body is
subject, those which consist in a change in the external conditions form a special group. By "external conditions" we mean in a wide sense various external fields. In practice the external conditions are most often determined by the fact that the body must have a prescribed volume. In one sense this case may also be regarded as a particular type of external field, since the walls which limit the volume are equivalent in effect to a potential barrier which prevents the molecules in the body from escaping.
If the body is subject to no interactions other than changes in external conditions, it is said to be thermally isolated. It must be emphasized that, although a thermally isolated body does not interact directly with any other
bodies, it is not in general a closed system, and its energy may vary with time.
In a purely mechanical way, a thermally isolated body differs from a closed system only in that its Hamiltonian (the energy) depends explicitly on the time: E = E(p, q, t), because of the variable external field. If the body also interacted directly with other bodies, it would have no Hamiltonian of its own, since the interaction would depend not only on the co-ordinates of the molecules of the body in question but also on those of the molecules in the other bodies.
This leads to the result that the law of increase of entropy is valid not only for closed systems but also for a thermally isolated body, since here we regard the external field as a completely specified function of co-ordinates and time, and in particular neglect the reaction of the body on the field. That is, the field is a purely mechanical and not a statistical object, whose entropy can in this sense be taken as zero. This proves the foregoing statement.
Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. Such a process is said to be adiabatic. We shall show that, in an adiabatic process, the entropy of the body remains unchanged, i.e. the process is reversible.
we will model the spaceship as an idealized box with perfectly reflecting walls. This is necessary, because the second law of thermodynamics applies only to thermally isolated systems, to which we can assign a Hamiltonian [5, section 11] [Landau L and Lifshitz E 1980 Statistical Physics vol 5, 3 edn (Pergamon)].
Chasing down that source: https://ia802908.us.archive.org/31/items/ost-physics-landaul...
ยง11. Adiabatic processes
Among the various kinds of external interactions to which a body is subject, those which consist in a change in the external conditions form a special group. By "external conditions" we mean in a wide sense various external fields. In practice the external conditions are most often determined by the fact that the body must have a prescribed volume. In one sense this case may also be regarded as a particular type of external field, since the walls which limit the volume are equivalent in effect to a potential barrier which prevents the molecules in the body from escaping.
If the body is subject to no interactions other than changes in external conditions, it is said to be thermally isolated. It must be emphasized that, although a thermally isolated body does not interact directly with any other bodies, it is not in general a closed system, and its energy may vary with time.
In a purely mechanical way, a thermally isolated body differs from a closed system only in that its Hamiltonian (the energy) depends explicitly on the time: E = E(p, q, t), because of the variable external field. If the body also interacted directly with other bodies, it would have no Hamiltonian of its own, since the interaction would depend not only on the co-ordinates of the molecules of the body in question but also on those of the molecules in the other bodies.
This leads to the result that the law of increase of entropy is valid not only for closed systems but also for a thermally isolated body, since here we regard the external field as a completely specified function of co-ordinates and time, and in particular neglect the reaction of the body on the field. That is, the field is a purely mechanical and not a statistical object, whose entropy can in this sense be taken as zero. This proves the foregoing statement.
Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. Such a process is said to be adiabatic. We shall show that, in an adiabatic process, the entropy of the body remains unchanged, i.e. the process is reversible.
I am unable to make these statements coherent