I don't believe the equation E=mc<sup>2</sup> violates any law of thermodynamics.
But there is an issue here that needs to be addressed and which I think is being widely misinterpreted.
E=mc<sup>2</sup> does
not say that matter and energy are the same thing. What it
does say is that a certain amount of energy is obtained when a certain amount of matter is annihilated which is a different thing entirely.
But there is a further problem in the use of the word "amount". We assume that "mass" and "energy" are quantities of "substances" - and this interpretation is too simplistic. Energy is not some kind of "magic liquid", we can't go and fill up a gallon jar with "energy". Nor could we do so with mass. Rather, mass and energy are names we give to particular manifestations or aspects of something more fundamental. Soapy Sam hit the nail on the head when he mentioned that they are aspects of the same thing.
The two faces of a coin are both "aspects" of the coin. But they are neither equal, equivalent or interchangeable. They are distinct and different, and observation of them depends on the frame of reference of the observer. Imagine a coin suspended in mid-air so that an observer on one side sees the heads and an observer on the other side sees the tails. Now, we can agree that they are
both looking at a coin - the coin is the fundamental object in question. But they will disagree on an apparent aspect of the coin - if we ask each which side is facing them, one will say "heads", the other will say "tails". It would be silly to deny this and say, "Well heads is the same as tails", because it clearly isn't. Nor could we say, "The total amount of sides is two and therefore we shall blur the distinction between one side and the other". Well, we could
say it, but it would be a lousy argument!
Therefore, in respect of energy/mass it would be more accurate to say that they are both superficial aspects of something fundamental. Different and distinct aspects, that depend on something unique to a particular observer. So we need to start by identifying the fundamental thing that we're looking at, and then look at what distinguishes one observer from another.
I believe the
fundamental thing is momentum. If we start from the assumption that all things in the universe have a property which we call momentum, it starts to make sense. But what is "momentum"? Isaac Newton thought it was fundamental too, he defined it as, "a quantity of motion". Which, despite its simplicity is a rather good definition.
Let us start with two objects. Each has a fundamental property of momentum. We place an observer on one of the objects. From the point of view of that observer we can now define "mass" and "energy" as relative aspects of momentum.
Assuming our observer is on object A:
1. If the object B is in net motion (not conservative motion) relative to object A, then object B appears to have a quality we call "energy".
2. If the object B is stationary relative to object A, then object B appears to have a quality we call "mass".
Superficially, this appears to be a pretty weak and useless definition - but
think about it. It's much more subtle than it appears.
The situation is analogous to electric and magnetic fields. If an observer is stationary with respect to an electric field, he sees only an electric field. If the observer is in motion relative to an electric field, he sees a magnetic field (and a changing electric field). In this latter case, it is actually the magnetic field that is equivalent to the momentum. The question of whether electric and magnetic fields are independent entities rather than just aspects of the same thing dependent on motion, is the same question (in form, if not substance) to the questions of mass/momentum/energy.