Identical Log Sequence Numbers
Was it due to the fact that there was no changes made ?


Yes, it's your case.


  When can i find out that the log sequence has been broken ?


You can do smth like this:

select database_name, 
       first_lsn, 
       last_lsn,
       lag(last_lsn) over (order by first_lsn) as prev_last_lsn
from msdb..backupset
where type = 'L' and database_name = 'yourDB'
order by first_lsn;


In unbroken log backup chain first_lsn = prev_last_lsn as every next lob backup starts where the previous backup stopped.

In your case the chain is unbroken.


  Having said that, even the action of taking a backup will normally
  cause an increment to the LSN


This is not true.

Log backup does not write anything to the log.

Full and differential do write to the log as they always do checkpoint at the beginning, so they write checkpoint operation to the log. 

And in fact, after the Full backup in OP we see that the next log backup has changed its LastLSN.