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Entropy information theory12/9/2023 ![]() The second law seems then to be just about statistics: It’s a law of large numbers. Many-particle systems that are more disordered and have higher entropy vastly outnumber ordered, lower-entropy states, so molecular interactions are much more likely to end up producing them. The implication is that eventually heat will be spread completely uniformly and there will be no driving force for further change - a depressing prospect that scientists of the mid-19th century called the heat death of the universe.īoltzmann’s microscopic description of entropy seems to explain this directionality. In this view, time seems to flow from past to future because the universe began - for reasons not fully understood or agreed on - in a low-entropy state and is heading toward one of ever higher entropy. This directionality is widely considered to impose an arrow of time. But the second law implies that change must happen in a way that increases entropy. At the level of individual particles, the classical laws of motion can be reversed in time. The second law appears to show why change happens in the first place. Entropy is loosely equated with disorder, but the Austrian physicist Ludwig Boltzmann formulated it more rigorously as a quantity related to the total number of microstates a system has: how many equivalent ways its particles can be arranged. More commonly this is expressed in terms of entropy, which must increase overall in any process of change. The first says that energy is always conserved the second law says that heat always flows from hot to cold. Instead, it became one of the central pillars of modern physics, providing criteria that govern all processes of change.Ĭlassical thermodynamics has only a handful of laws, of which the most fundamental are the first and second. In the end, thermodynamics wasn’t much help in making better engines and machinery. The need for such a theory was urgently felt as steam power drove the Industrial Revolution, and engineers wanted to make their devices as efficient as possible. Thermodynamics was conceived in the early 19th century to describe the flow of heat and the production of work. It is a logical consequence of the most fundamental resource that we know of - the quantum resource of information. In this telling, an increase in entropy is not just the most likely outcome of change. It arises from the ways in which quantum systems share information, and from cornerstone quantum principles that decree what is allowed to happen and what is not. According to this view, the second law comes about not because of classical probabilities but because of quantum effects such as entanglement. They may have woven the second law out of the fundamental principles of quantum mechanics - which, some suspect, have directionality and irreversibility built into them at the deepest level. Can the second law be tightened up into more than just a statement of likelihoods?Ī number of independent groups appear to have done just that. “We like laws of physics to be exact,” said the physicist Chiara Marletto of the University of Oxford. Yet physicists don’t just want descriptions of what will probably happen. Although it’s called a law, it’s usually regarded as merely probabilistic: It stipulates that the outcome of any process will be the most probable one (which effectively means the outcome is inevitable given the numbers involved). Some are not convinced that we understand it properly or that its foundations are firm. ![]() ![]() But if your theory is found to be against the second law of thermodynamics I can give you no hope there is nothing for it but to collapse in deepest humiliation.” No violation of this law has ever been observed, nor is any expected.īut something about the second law troubles physicists. “If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations - then so much the worse for Maxwell’s equations,” wrote the British astrophysicist Arthur Eddington in his 1928 book The Nature of the Physical World. ![]() In information theory, the cross-entropy between two probability distributions p ).In all of physical law, there’s arguably no principle more sacrosanct than the second law of thermodynamics - the notion that entropy, a measure of disorder, will always stay the same or increase. ![]()
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