This question is kind of self-explanatory, but for people who are physicists, if a time reversible rule of physics/cellular automaton exists in a world, does this automatically imply the first law of thermodynamics, that is energy may not be created or destroyed?
Note I’m not talking about time-symmetry or the 2nd law of thermodynamics, which states that you can’t have a 100% efficient machine, just time-reversible physical laws/cellular automatons and the first law of thermodynamics.
Edit: @jacob_drori has clarified what exactly I’m supposed to be asking, so the edited question is this:
Do you always get time-symmetric physical laws that are symmetric for any T, out of time-reversible physical laws?
The question of do you always get time-symmetric physical laws from time reversible laws is also a valid question to answer here, but the important part for the first law of thermodynamics to hold is that it’s symmetric for all times T, and in principle, the question of time reversible laws of physics always implying time symmetry could have a positive answer while having a negative answer to the original question, because it doesn’t imply time symmetric laws of physics for all T.
[Question] Does a time-reversible physical law/Cellular Automaton always imply the First Law of Thermodynamics?
This question is kind of self-explanatory, but for people who are physicists, if a time reversible rule of physics/cellular automaton exists in a world, does this automatically imply the first law of thermodynamics, that is energy may not be created or destroyed?
Note I’m not talking about time-symmetry or the 2nd law of thermodynamics, which states that you can’t have a 100% efficient machine, just time-reversible physical laws/cellular automatons and the first law of thermodynamics.
Edit: @jacob_drori has clarified what exactly I’m supposed to be asking, so the edited question is this:
Do you always get time-symmetric physical laws that are symmetric for any T, out of time-reversible physical laws?
The question of do you always get time-symmetric physical laws from time reversible laws is also a valid question to answer here, but the important part for the first law of thermodynamics to hold is that it’s symmetric for all times T, and in principle, the question of time reversible laws of physics always implying time symmetry could have a positive answer while having a negative answer to the original question, because it doesn’t imply time symmetric laws of physics for all T.