(Mentioned in "Entropy"). Firstly, entropy is the amount of disorder or randomness in a system. A "system" can be anything. If your system is a small balloon full of air, then you can measure the amount of disorder in your balloon. Entropy is usually measured in Joules/Kelvin. It can be used in thermodynamics to determine whether or not (and to what magnitude) a process will happen all by itself, without any external influences (whether or not the process is spontaneous). All spontaneous processes result in an increase in the total combined entropy (or disorder) of a system and its surroundings. This is shown by the second law of thermodynamics. There are always more disordered states than ordered states, so disorder always happens naturally.). According to physics, entropy (sort of) gives time its forward direction because the entropy of the universe always increases as time moves forward. It is impossible to go backwards in time because it would decrease the entropy of the universe (which the second law of thermodynamics will not allow). In the song ("Entropy") Greg sings, "We're in a play of slow decay orchestrated by Boltzmann, it's entropy...". Ludwig Boltzmann was an Austrian physicist. Basically, he said that the entropy of any given state is related to the number of ways that the state can be acheived. If a state can be acheived in a lot of different ways, it has higher entropy than a state that can be acheived in a smaller number of ways. This is also known as "positional disorder." His equation for calculating entropy is: S = k ln W. S is the entropy of the state in Joules / Kelvin degrees. W is the number of ways that the state can be acheived. k is Boltzman's constant. It is 1.38 e-23 J/K (rounded). Boltzmann's constant was derived by dividing the gas law constant, R, by Avagadro's number. [8.314(J/(moles*Kelvin)] / [6.02e23 (particles/mole)]. The moles cancel and you're left with 1.38 e-23 J/K.
The second law of thermodynamics shows that all processes result in an increase in the disorder (entropy) of the universe. The entropy of the universe cannot decrease. So the song is connected to the idea that at some far away time in the far distant future, all will be disorder and the universe as we know it will have to come to an end. There will be no order or free energy left. So when Greg sings "We're in a play of slow decay orchestrated by Boltzmann," we know that we are slowly but surely losing the order in the universe as time moves forward. Eventually, all will be disorder. The universe will not reach equilibrium until this happens. There's nothing we can do about it. It's not a human issue.