The definition of entropy, S is
dS = (dQ/T)rev
showing that the differential change in entropy, dS, in a process is equal to the ratio of the differential amount of heat interaction, dQ, that takes place if the process is reversible and the absolute temperature, T, during that process.
The entropy of real isolated systems always rises. Through some operational arguments, but primarily by using statistical mechanics on the molecular level, entropy was shown to be a measure of disorder. This supports the observation that isolated systems undergoing any process become less orderly; mess increases unless an external agent is employed to make order, all consistent with the entropy increase law. Profoundly, entropy is thus regarded to be the scientific indicator of the direction of time - "the arrow of time", after Eddington. The inevitable increase of disorder/entropy with time has led to deeper questions about the origin of the world and indeed of time itself, about the future of the universe in which disorder continuously grows, perhaps to a state of utter disorder (i.e. death), and has raised much philosophical discourse related to these issues. Significant attempts have been made to relate entropy and the second law of thermodynamics to almost any human endeavour, including communications, economics, politics, social science, and religion, not always in a scientifically convincing manner.
Main page for Science and Engineering