Entropy magazine11/24/2023 ![]() ![]() Hopefully I managed to get all the various increasing/decreasing pointing in the right direction. Without the 140-character limit, it's hard to stop typing, even if I try to just link and give a very terse explanation. But the interpretation is that the population is "learning" more and more about the stable state, until it achieves that state and knows all there is to know! Okay, you can see why tweeting is seductive. Since information is minus entropy, this is a Second-Law-like behavior. Then the take-home synthesis is this: if you are not in an evolutionarily stable state, then as your population evolves, the relative information between the actual state and the stable one decreases with time. An equilibrium configuration, we might say. ![]() ![]() Then there is something called an evolutionarily stable state, one in which the relative populations (the fraction of the total number of organisms in each species) is constant. That is: imagine that every member of the population breeds at some rate that depends on circumstances. Make the natural assumption that the rate of change of a population is proportional to the number of organisms in that population, where the "constant" of proportionality is a function of all the other populations. The second point has to do with the evolution of populations in biology (or in analogous fields where we study the evolution of populations), following some ideas of John Maynard Smith. The relative information between two distributions can be thought of as how much you don't know about one distribution if you know the other one the relative information between a distribution and itself is zero. (Aside to experts: I'm kind of shamelessly mixing Boltzmann entropy and Gibbs entropy, but in this case it's okay, and if you're an expert you understand this anyway.) John explains that the information (and therefore also the entropy) of some probability distribution is always relative to some other probability distribution, even if we often hide that fact by taking the fiducial probability to be uniform (. If it's high-entropy, there are many states that look that way, so you don't have much information about it. Information can be thought of as "minus the entropy," or even better "the maximum entropy possible minus the actual entropy." If you know that a system is in a low-entropy state, it's in one of just a few possible microstates, so you know a lot about it. It's the idea of "relative entropy" and its equivalent "information" formulation. The first is a bit of technical background you can ignore if you like, and skip to the next paragraph. Electrochemical batteries are currently a major enabler in the energy transition however, batteries involve redox reactions during charging/discharging, thereby limiting their primary use in applications with relatively steady and ‘slow’ energy output (for example, portable electronics and electric vehicles).Okay, sticking to my desire to blog rather than just tweet (we'll see how it goes): here's a great post by John Baez with the forbidding title "Information Geometry, Part 11." But if you can stomach a few equations, there's a great idea being explicated, which connects evolutionary biology to entropy and information theory. There is broad demand to accelerate the transition to more efficient, less polluting, and renewable energy sources such as solar and wind energy, but these sources often cannot produce energy all the time. ![]() Recovering the stored energy requires breaking and forming new chemical bonds (typically via combustion) and, while this can be effective, it can also produce pollution that contributes to climate change. BE WARNED THAT PROVIDING THIS MAGAZINE TO, OR READING IN THE PRESENCE OF, MINORS MAY CONSTITUTE A CRIMINAL OFFENCE. The challenge of storing energy is not new, and for generations, we have relied on chemical approaches (that is, energy is stored in the arrangement of atoms in molecules, as in carbon-based fuels) to this end. entropy magazine is to be read only by persons 18 years and older. We face a colossal energy storage problem with analysts predicting a more than 120-times increase in global energy storage needs by 2040 1. ![]()
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