I am very new to this business about entropy, so I came up with the following experiment to make sense of what I understood.

A gas in some volume $V$ initially expands into a gas in volume $2V$. We say there is entropy increment of $(k_B)N\log2$ in this process. On the other hand, if I know the resulting gas in volume $2V$, I can time reverse so that I know the initial configuration and vice versa. This is the main idea of information conservation, I think, as stated in here

This seems to suggest that Entropy of gas which we know have expanded from volume $V$ is same as entropy of gas in volume $V$ since they are in bijection. Because of the entropy increment above, then can we conclude that there are certain configurations of gas inside the volume $2V$ which have not and will not end up completely in the volume $V$, cuz otherwise both systems would have same entropy (i.e not differ by $N\log2$ amount entropy)?

That would explain the statement "why doesn't a gas system doesn't just shrink to a configuration in much smaller volume usually". Is that correct interpretation?

I am very new to this business about entropy, so I came up with the following experiment to make sense of what I understood.

A gas in some volume $V$ initially expands into a gas in volume $2V$. We say there is entropy increment of $(k_B)N\log2$ in this process. On the other hand, if I know the resulting gas in volume $2V$, I can time reverse so that I know the initial configuration and vice versa. This is the main idea of information conservation, I think, as stated in here

This seems to suggest that Entropy of gas which we know have expanded from volume $V$ is same as entropy of gas in volume $V$ since they are in bijection. Because of the entropy increment above, then can we conclude that there are certain configurations of gas inside the volume $2V$ which have not and will not end up completely in the volume $V$, cuz otherwise both systems would have same entropy (i.e not differ by $N\log2$ amount entropy)?

That would explain the statement "why doesn't a gas system doesn't just shrink to a configuration in much smaller volume usually". Is that correct interpretation?

I am very new to this business about entropy, so I came up with the following experiment to make sense of what I understood.

A gas in some volume $V$ initially expands into a gas in volume $2V$. We say there is entropy increment of $(k_B)N\log2$ in this process. On the other hand, if I know the resulting gas in volume $2V$, I can time reverse so that I know the initial configuration and vice versa. This is the main idea of information conservation, I think, as stated in here

This seems to suggest that Entropy of gas which we know have expanded from volume $V$ is same as entropy of gas in volume $V$ since they are in bijection. Because of the entropy increment above, then can we conclude that there are certain configurations of gas inside the volume $2V$ which have not and will not end up completely in the volume $V$, cuz otherwise both systems would have same entropy (i.e not differ by $N\log2$ amount entropy)?

That would make the statements about "why doesn't a gas system doesn't just shrink to its original configuration (sometimes)"

I am very new to this business about entropy, so I came up with the following experiment to make sense of what I understood.

A gas in some volume $V$ initially expands into a gas in volume $2V$. We say there is entropy increment of $(k_B)N\log2$ in this process. On the other hand, if I know the resulting gas in volume $2V$, I can time reverse so that I know the initial configuration and vice versa. This is the main idea of information conservation, I think, as stated in here

This seems to suggest that Entropy of gas which we know have expanded from volume $V$ is same as entropy of gas in volume $V$ since they are in bijection. Because of the entropy increment above, then can we conclude that there are certain configurations of gas inside the volume $2V$ which have not and will not end up completely in the volume $V$, cuz otherwise both systems would have same entropy (i.e not differ by $N\log2$ amount entropy)?

That would explain the statement "why doesn't a gas system doesn't just shrink to a configuration in much smaller volume usually". Is that correct interpretation?