I am not quite sure to understand what you imply by "emergent degrees of freedom relevant to the 2nd law of thermodynamics". The 2nd law is about entropy and irreversibility. Entropy may be understood as being monotonically related to the number of available states of motion at a given energy (in the "thermodynamic limit" this number is monotonically growing with energy). I am not sure how the concept of "relevant degree of freedom" would (have to) enter here.

This said, I can affirm that the entropy does change in the transition to the superconducting state over and above what would happen in absence of the transition. As a consequence, a discontinuity is observed in the specific heat of superconductors at the critical temperature (Tc).

It is also true that the character of the available degrees of freedom does indeed change. According to the BCS description of superconductivity Cooper pairs form. Pair formation introduces a correlation between the movements of electronic quasiparticles below Tc which are essentially uncorrelated above Tc. They give up their uncorrelatedness (-> state of higher entropy) for a gain in energy (-> BCS gap). The total number of states of motion must stay unchanged, however and therefore for every lowered state, there is one of increased energy (-> BCS density of states, note the analogy to the formation of bonding and antibonding states in molecules), essentially unoccupied, though. The superconducting state is therefore said to be more ordered than the normal state. A measure of the degree of ordering is the number density of Cooper pairs. All these things have been experimentally verified.

Setting up the Meissner state now corresponds to a center of mass movement of Cooper pairs. The current is persistent as long as the kinetic energy involved in that movement does not exceed the binding energy of the Cooper pair. The cooper pair is protected from inelastic scattering events involving less energy transfer than the pair binding energy. THIS is one important difference to states of motion of non-paired electrons. [Halas, I'm simplifying things here, though!]

Hypothetical ideal conductors (zero resistivity, no Cooper pairs) would display an analogous diamagnetism to the one of superconductors upon switching on a magnetic field or upon being moved from a spatial region with B=0 to one with B0. This is because both processes involve nonzero electrical fields (-> Maxwell's equations) which accelerate single electrons and Cooper pairs alike. The truly special point about superconductors is that the current carrying state is formed even upon cooling through Tc alone (no movement or B change). Obtaining this result, however, requires computing the many body state of motion in the presence of the magnetic field (or the associated vector potential). This is beyond what can be described here. You may choose S. Elliotts book on "Physics and Chemistry of Solids" as an excellent initial read.

I've been that long just to try saying that yes, the superconducting state is set up by other (correlated) states of motion (= emergent degrees of freedom?).The associated entropy is reduced, the heat capacity changed (-> 2nd law). The states of motion would also be possible in a normal conductor, but they don't survive, because they are not protected by the Cooper pair binding energy. This simplified version of the story dos not tell the whole magic of the Meissner effect, though, which requires understanding the superconducting state as a macroscopic, many-Cooper-pair quantum state.

Dear Fauth, Many thanks for your informative and challenging answer to the above question. I found your reply both useful and stimulating to my further reading in related sources. I would not want to place too much stress upon "emergence" in my question, in light of your reply. ( I think to explain or exemplify "emergence" by reference to the properties of chemical compounds being so distinct from those of the combining elements.)

I take a key phrase from you, and would prefer to rephrase my question (as I just did a related question) in terms of "available degrees of freedom." Entropy tends to increase, in general terms, because the possible disordered states of a given system are much more numerous than the possible ordered states --and hence more likely --in statistical mechanics. But, my thinking was, if we get a change in the (available) degrees of freedom of a system, then this would also effect the likely evolution of the system. Something otherwise very unlikely might become more likely. I was thus particularly encouraged by your statement that "It is also true that the available degrees of freedom do indeed change (with the formation of the Cooper pairs.) You also write that "The superconducting state is therefore said to be more ordered than the normal state." This I take it, is because of the pairwise movement of electrons, (converted, as it were from fermions into boson-like entities) are no longer constrained by the Pauli exclusion principle? You mention at the end of your reply that "the superconducting state [is] a macroscopic many-Cooper-pair quantum state", and this strikes me as a fascinating point directly related to longer-range relations of the Cooper pairs--something, again, which emerges below Tc.

I won't try to say more just now, though I think I've left much out, except to say that I stand to learn a lot of physics here. I will have to take a break for a few days of travel. Again, many thanks for your stimulating reply.

There is a rather simple explanation for the Meissner effect that I worked out using field-free electrodynamics based on the Weber force. It may be found here:

Article Meissner Effect in Classical Physics