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I have stumped myself with a thought experiment of my own devising. Suppose I take a beam of wholly depolarised, but otherwise plane wave light. Its von Neumann entropy per photon is $\log(2)$ nats o …

The temperature is that of both the system and surroundings. The whole point of "free energies" is that you must imagine: The system to be in thermodynamic equilibrium at all times so that, a fortio …

There are several ways to do this, but you are severely limited by the second law of thermodynamics. …

As in the comments, you need to specify the probability distribution for the electron eigenstates. This distribution can depend on the hydrogen atom's environment - if the hydrogen atom is in a resona …

What I do not understand is the engine does work, which is a form of energy transfer where energy leaves the engine, so why can we not have an engine where the work done by it restores its entropy, …

Another way of getting at Valter Moretti's answer using a somewhat outdated (but altogether rigorous) notion of generalized functions is simply to witness that: $$\int_{-\infty}^\infty T(x, t)\,\math …

But one can also derive the formula from EM theory without thermodynamics. R. E. …

"Measurement of Disorder" is not a particularly good metaphor for entropy. Your title suggestion is closer to a sounder notion: in these terms I would call entropy a measure of "progress towards therm …

A "good" definition (although the term is vague) must replicate at least some of our major intuitions about the notion that is being defined. A very fundamental everyday thing that a scientist gropin …

The second law of thermodynamics in optics is equivalent to the non-decreasing of étendue, which is the volume of a system of rays representing a light field in optical phase space and thus a measure …

So this is part of the answer, but really we need physics - thermodynamics - insight. The reason comes from the definition of temperature and its relationship with the second law of thermodynamics. … one of the little Carnot cycles: what this means is that we'd have a reversible heat engine with a different efficiency from the Carnot cycle, which gainsays Carnot's theorem and thus the second law of thermodynamics …

The Earth's surface, and the atmosphere, is in thermal contact with outer space, with the heat transfer mechanism being radiation. The Earth-atmosphere system is constantly losing heat by this mechani …

Definitions First and foremost, temperature is a parameter defining a statistical distribution, much as the statistical parameters of mean and standard deviation define the normal probability distrib …

Snow is simply a random collection of snowflakes and bits of irregularly shapen bits of ice. Each of these is clear, but a small fraction of the light incident on each clear entity is reflected and sc …

The bare Boltzmann formula is a bit basic to make sense of for a lone electron. You need to talk about a generalization: one thinks in terms of the Shannon entropy of the state. We also need to be ca …