Natural laws reflect our empirical knowledge about "nature" (as opposed to the world of human society). So actually there is no "proof" of, say, energy conservation. Nevertheless the kind of empirical knowledge that is expressed in physical laws is extraordinarily reliable. If one ever observes a process where energy seems not to be conserved, she confidently should believe in a ghost carrying away that lacking amount of energy instead of failure of energy conservation. That is exactly what Wolfgang Pauli did; in the beta-decay of radioactivity, energy (and angular momentum) seemed not to be conserved. So he postulated a "ghost", a particle, that carried that energy away, the neutrino. Its existence was in fact proved experimentally some years later.
So energy and entropy are concepts that let us state some constraints to the universe of possible processes. From the concept of energy we can state that "real" processes must obey energy conservation, whereas the concept of entropy narrows the amount of "real" processes further. The two concepts are similar in this sense. The difference is psycologic, most of us are familiar with the concept of energy, few with the concept of entropy.
Considering chemical systems, it is often stated that, for a process to take place, the system must be able to decrease its total energy. More exactly, if a system can decrease its internal energy by a given process, this process may take place even if the systems entropy decreases.
On the other hand, if the system is to increase its internal energy by a given process, then this process may take place only if systems entropy increases as well.
Let us have a closer look at a system that is going to decrease its internal energy by some process. The system is said to be in a more stable state as soon as its internal energy has lowered. As a simple example, consider an asteroid falling down to earth, the system being earth and asteroide.
When the asteroide impacts on earths surface, its kinetic energy is dissipated, and the internal energy of the system is lowered. Hence it is in a more stable state.
Why is a low energy state more stable than a high energy state?
The answer can be found by an entropy analysis. By the impact of the asteroid, much of the its kinetic energy is radiated out as heat. That is, plenty of low energy photons are generated that carry away the energy. Compared to the number of photons, the contribution of debris to total entropy can probably be neglected.
Now many particle system is more probable than a system of few particles, just as a broken glass is more probable than a solid one. There are more ways to arrange, say, ten pieces of a broken glass than the glass as a whole.
It turns out that the low energy state is more stable only in a cold universe, where entropy increases by the dissipation of heat. Would the universe be hot, then total entropy would increase if the system would absorb energy rather than to dissipate it.
The bottom line is that entropy, not energy, is the most fundamental quantity that governs physical processes.
Last updated Mar. 16, 1999, GVa