Is that phrase true?
"Each process has its logical PC, but the processor has only one physical PC. "
Could you justify the claim?
That phrase is not something you will have seen written anywhere by us as in FreeRTOS we talk about tasks rather than processes and threads.
The program counter (PC) register holds the address of the next instruction to execute. If your process only has a single core then there is only one physical program counter in the physical device. Then, if you only have one thread of software execution there is only ever one value of PC in use (ignoring interrupts) as there is only ever one next instruction that will be executed, and the PC value does not need to be saved by software. If you have multiple threads of execution then each thread has its own copy of the next instruction to be executed, so each thread saves (in software) its own copy of the PC register.