Second law of thermodynamics

Consider two isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium in itself (but not in equilibrium with each other). Then let some event break the isolation that separates the two systems, so that they become able to exchange matter or energy. Wait till the exchanging systems reach mutual thermodynamic equilibrium. Then the sum of the entropies of the initial two isolated systems is less than or equal to the entropy of the final exchanging systems. In the process of reaching a new thermodynamic equilibrium, entropy has increased (or at least has not decreased). Both matter and energy exchanges can contribute to the entropy increase.

In a few words, the second law states "spontaneous natural processes increase entropy overall." Another brief statement is "heat can spontaneously flow from a higher-temperature region to a lower-temperature region, but not the other way around." Nevertheless, energy can be transferred from cold to hot, for example, when a refrigerator cools its contents while warming the surrounding air, though still all transfers as heat are from hot to cold. Heat flows from the cold refrigerator air to the even-colder refrigerant, then the refrigerant is warmed by compression (which requires an external source of energy to do thermodynamic work), then heat flows from the hot refrigerant to the outside air, then the refrigerant cools by expansion to its initial volume (thus doing thermodynamic work on the environment), and the cycle repeats. Entropy is increased also by processes of mixing without transfer of energy as heat.

A way of thinking about the second law is to consider entropy as a measure of ignorance of the microscopic details of the motion and configuration of the system given only predictable reproducibility of bulk or macroscopic behaviour. So, for example, one has less knowledge about the separate fragments of a broken cup than about an intact one, because when the fragments are separated, one does not know exactly whether they will fit together again, or whether perhaps there is a missing shard. Solid crystals, the most regularly structured form of matter, with considerable predictability of microscopic configuration, as well as predictability of bulk behaviour, have low entropy values; and gases, which behave predictably in bulk even when their microcopic motions are unknown, have high entropy values. This is because the positions of the crystal atoms are more predictable than are those of the gas atoms, for a given degree of bulk predictability.