On average it would be expected that the smoke particles around a struck match would drift away from each other, diffusing throughout the available space.
It is only when the gas is studied at a macroscopic scale that the effects of entropy become noticeable. As it drifts left or right, qualitatively it looks no different. 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. When studying at a microscopic scale, the above judgements cannot be made. Because of the second law of thermodynamics, entropy prevents macroscopic processes showing T-symmetry. 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.
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. 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. For example, it is often very easy to tell the difference between a video being played forwards or backwards. Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy. Stephen Hawking, A Brief History of Time “The increase of disorder or entropy is what distinguishes the past from the future, giving a direction to time.” In thermodynamic systems that are not closed, entropy can decrease with time, for example living systems where local entropy is reduced at the expense of an environmental increase (resulting in a net increase in entropy), the formation of typical crystals, the workings of a refrigerator and within living organisms. Thus, entropy measurement is a way of distinguishing the past from the future. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time.
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