where does entropy-increasing waste heat go during non-reversible processes?
The first law of thermodynamics states that energy is conserved. $\Delta U = Q - W$ (internal energy change is the difference between external energy supplied and work done on the environment).
The second law of thermodynamics states that entropy is never decreasing and is only constant in reversible thermodynamic processes. In a non-reversible thermodynamic process, the entropy of the universe is increased.
Suppose we have an abstract 1-dimensional cellular automata universe consisting of 0s (empty space) and 1s (energy/atoms) but obeying the first and second laws of thermodynamics. The 1s are drawn together via "gravity" forces:
t0: 0010000100 t1: 0001001000 t2: 0000110000
Unlike microscopic time-reversible phenomena, let us assume that the collision of the two 1s generates entropy.
Q1: Would the final state of this universe be cycling through all possible $10 \choose 2$ states, as that is the maximum entropy configuration?
Q2: If the answer to Q1 is yes, then that implies a set of dynamics that encourage an equilibrium distribution of two 1s over the 10 position. 749
If we have any less or more than 2 1s, wouldn't that violate conservation of energy? (the total energy of the starting system is 2).
Q3: Where does entropy "go" when it is produced? In this toy universe I have no way to embody any other non-zero energy than "1". If we choose to introduce a new letter "H" as an "entropy" particle, does this violate the first law of thermodynamics? (since the new energy of the system is 1 + 1 + H). Does entropy occupy space?
t1: 0001001000 t2: 000011H000
Or is it a "hidden state" a cell that follows energy around?
The bigger question here is that when I think of living things perform some thermodynamically irreversible work to lower their entropy, I am wondering where that entropy "goes". If entropy is created but mass and energy are conserved, how do we end up with heat "for free" without changing total energy?
``` t1: 0001001000 h1: 0000000000
t2: 0000110000 h2: 00000H0000 ```
Q4: Are random dynamics required here in order to eventually reach a state of maximum entropy? One way to model this would be to treat H as "non-useful work" that fills up the universe and potentially creates more H when it interacts with non-H cells.
Q5: Are there any limitations to this 1D universe in my understanding of how the first and second law of thermodynamics works? 749