Entropy as an arrow of time

Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Thus, entropy measurement is a way of distinguishing the past from the future. In thermodynamic systems that are not isolated, local entropy can decrease over time, accompanied by a compensating entropy increase in the surroundings; examples include objects undergoing cooling, living systems, and the formation of typical crystals. Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy. For example, it is often very easy to tell the difference between a video being played forwards or backwards. A video may depict a wood fire that melts a nearby ice block, played in reverse it would show that a puddle of water turned a cloud of smoke into unburnt wood and froze itself in the process. Surprisingly, in either case the vast majority of the laws of physics are not broken by these processes, a notable exception being the second law of thermodynamics. When a law of physics applies equally when time is reversed, it is said to show T-symmetry; in this case, entropy is what allows one to decide if the video described above is playing forwards or in reverse as intuitively we identify that only when played forwards the entropy of the scene is increasing. Because of the second law of thermodynamics, entropy prevents macroscopic processes showing T-symmetry. When studying at a microscopic scale, the above judgements cannot be made. Watching a single smoke particle buffeted by air, it would not be clear if a video was playing forwards or in reverse, and, in fact, it would not be possible as the laws which apply show T-symmetry. As it drifts left or right, qualitatively it looks no different; it is only when the gas is studied at a macroscopic scale that the effects of entropy become noticeable (see Loschmidt's paradox).