Entropy (arrow of time)

Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires 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. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However, in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms, used in thermodynamics. Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires 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. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However, in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms, used in thermodynamics. 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 can not 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 you study that gas at a macroscopic scale that the effects of entropy become noticeable. On average you would expect the smoke particles around a struck match to drift away from each other, diffusing throughout the available space. It would be an astronomically improbable event for all the particles to cluster together, yet you can not comment on the movement of any one smoke particle. By contrast, certain subatomic interactions involving the weak nuclear force violate the conservation of parity, but only very rarely. According to the CPT theorem, this means they should also be time irreversible, and so establish an arrow of time. This, however, is neither linked to the thermodynamic arrow of time, nor has anything to do with our daily experience of time irreversibility. The Second Law of Thermodynamics allows for the entropy to remain the same regardless of the direction of time. If the entropy is constant in either direction of time, there would be no preferred direction. However, the entropy can only be a constant if the system is in the highest possible state of disorder, such as a gas that always was, and always will be, uniformly spread out in its container. The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the 'past'. Thus this law is about the boundary conditions rather than the equations of motion of our world. The Second Law of Thermodynamics is statistical in nature, and therefore its reliability arises from the huge number of particles present in macroscopic systems. It is not impossible, in principle, for all 6 × 1023 atoms in a mole of a gas to spontaneously migrate to one half of a container; it is only fantastically unlikely—so unlikely that no macroscopic violation of the Second Law has ever been observed. T Symmetry is the symmetry of physical laws under a time reversal transformation. Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics. The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the early universe. According to the Big Bang theory, the Universe was initially very hot with energy distributed uniformly. For a system in which gravity is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into black holes, a state to which the system may eventually evolve). As the Universe grows, its temperature drops, which leaves less energy available to perform work in the future than was available in the past. Additionally, perturbations in the energy density grow (eventually forming galaxies and stars). Thus the Universe itself has a well-defined thermodynamic arrow of time. But this does not address the question of why the initial state of the universe was that of low entropy. If cosmic expansion were to halt and reverse due to gravity, the temperature of the Universe would once again grow hotter, but its entropy would also continue to increase due to the continued growth of perturbations and the eventual black hole formation, until the latter stages of the Big Crunch when entropy would be lower than now. Consider the situation in which a large container is filled with two separated liquids, for example a dye on one side and water on the other. With no barrier between the two liquids, the random jostling of their molecules will result in them becoming more mixed as time passes. However, if the dye and water are mixed then one does not expect them to separate out again when left to themselves. A movie of the mixing would seem realistic when played forwards, but unrealistic when played backwards.