I think it is mostly a matter of definitions. I am not familiar with your terminology. Also, if I have an atom that is in unknown alignment, and I align it using magnetic field, then take away the resulting heat, then the entropy (number of states) of that subsystem decreases, and this is used to attain extremely low temperatures. I am more familiar with the physical notion of entropy.
edit: Also, after powering electromagnet, I know that the direction of coin and direction of electromagnet relate in a particular way, which I did not know before. At the same time, I have physically restricted the number of states that the environment can be in—the coin can not now be other way around. It’s in this sense that entropy of environment (as seen on large scale) decreases . (and it is of course subjective, that the number of states that environment can be in, decreases. It does not decrease according to agent that already knows which way the coin is)
I think it is mostly a matter of definitions. I am not familiar with your terminology. Also, if I have an atom that is in unknown alignment, and I align it using magnetic field, then take away the resulting heat, then the entropy (number of states) of that subsystem decreases, and this is used to attain extremely low temperatures. I am more familiar with the physical notion of entropy.
edit: Also, after powering electromagnet, I know that the direction of coin and direction of electromagnet relate in a particular way, which I did not know before. At the same time, I have physically restricted the number of states that the environment can be in—the coin can not now be other way around. It’s in this sense that entropy of environment (as seen on large scale) decreases . (and it is of course subjective, that the number of states that environment can be in, decreases. It does not decrease according to agent that already knows which way the coin is)