# Tagged Questions

Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Maybe combine with [tag:statistical-mechanics].

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### Can Lee-Yang zeros theorem account for triple point phase transition?

Now the prominent Lee-Yang theorem (or Physical Review 87, 410, 1952) has almost become a standard ingredient of any comprehensive statistical mechanics textbook. If the volume tends to infinity, ...
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### Why does temperature change the friction coefficient of my stovetop?

I have a Ceran cooking field at home, it's a glass-ceramic surface with heating coils embedded beneath. When I slide a pan around there's much more friction on a hot plate than on a cool one. Why? ...
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### How to obtain the free energy of the canonical ensemble in Euclidean general relativity?

If the gravitational field couples with matter fields, such as a charged scalar field, I know the partition function of the grand canonical ensemble naturally relates to the path-integral expression ...
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### Lattice model completely constrained by boundary data

I am dealing with a lattice model that has the peculiar property that if I specify all the spins on the boundary, by local conservation laws, the whole lattice configuration (throughout the whole ...
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### experiment proposal to validate microcausality

I've been wondering about microcausality for some time now (a recent question of mine regarding the topic) and i'm wondering if its possible to devise an experiment to detect potential violations I ...
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### Hindered rotation model for flexible polymers: deriving the Flory characteristic ratio

In the hindered rotation model we assumes constant bond angles $\theta$ and lengths $\ell$, with torsion angles between adjacent monomers being hindered by a potential $U(\phi_i)$. In Rubinstein's ...
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### Violations of Onsager reciprocity?

As far as I understand it, the modern statement of Onsager reciprocity is that the linear-response transport coefficient matrix, when transposed, is equal to that of the time-reversed system (reversed ...
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### Radiative equilibrium in orbit of a black hole

According to Life under a black sun, Miller's planet from Interstellar, with a time dilation factor of 60,000, should be heated to around 890C by blue-shifted cosmic background radiation. How they ...
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### Thermodynamic equilibrium or thermal equilibrium and equipartition theorem

In all derivations of the equipartition theorem I can find a thermodynamic equilibrium distribution is used to show it's validity. But more vague sources (physics.stackexchange answer by Luboš Motl, ...
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### Nose-Hoover Barostat

Much can be found about the Nose-Hoover Thermostat. However I seem to be having difficulty finding out details about the Nose-Hoover Barostat, and how it is implemented. Would anyone be able to give ...
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### Dimensional inconsistency in first law of black hole thermodynamics

The first law of black hole mechanics (let's simplify by considering a uncharged and non-rotating black hole) can be written as $$\delta M = T \delta S$$ If I use the definition of Hawking ...
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### What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of Weaire–...
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### The surface area to volume ratio of a sphere and the Bekenstein bound

I am trying to relate the surface-area-to-volume-ratio of a sphere to the Bekenstein bound. Since the surface-area-to-volume-ratio decreases with increasing volume, one would surmise that, per unit of ...
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### A theoretical model for evaporation occurring when wind is blowing over the surface of water

I've recently done an experiment in which I was studying the variation of the cooling rate of hot water in a draft (wind). The air was blow directly over the surface of the water (kept in a ...
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I was reading CH3 of Reichl's "A Modern Course in Statistical Physics" on Ginzburg-Landau theory and don't really understand a couple of points he makes. He writes: I don't understand why the first ...
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### How to calculate the energy transfer between working coil and working piece and dissipated energy of working piece in induction heating?

For who don't know how does induction heating work, a short description can be found here. However, my question is about physics. Assume I have a coil inductor calculated carefully 50 uH as below: ...
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### How does air going through silica gel change its humidity

Assume that the properties(temperature,humidity,velocity and so on) of the incoming air flow stay constant. The air flow goes through a silica gel plate. Humidity of the air will decrease, but how to ...
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### Physical interpretation of the chemical potential in Bose and Fermionic gas

I understand that both Fermions and bosons have the chemical potential $\nu <0$ when it is T>0, but still behave classically, the fermions would increase its chemical potential at T=0, whereas the ...
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### A problem with ADM mass in the derivation of 1st law of black hole thermodynamics

The definition of ADM mass is $$M=\frac{1}{16\pi}\lim_{r\rightarrow\infty}\int \left(\frac{\partial h_{\mu\nu}}{\partial x^\mu}-\frac{\partial h_{\mu\mu}}{\partial x^\nu} \right)N^\nu dA$$ according ...
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### What happens to the observed thermal energy of objects at relativistic speeds?

When an object is observed to move near the speed of light, what difference in thermal energy is observed? Does time dilation imply that it's colder?
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### Free energy of coupled classical harmonic oscillators

I'm looking to find the thermodynamic (NVT) free energy of a classical coupled harmonic oscillator system such as the one below: (image taken from http://openmetric.org/StatisticalPhysics/...
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### Validity of topological thermodynamics?

I've been reading some material by R. Kiehn, developing a topological approach to non-equilibrium thermodynamics through Cartan forms, where the fundamental claim is that irreversible processes are ...
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### Coarse graining on measurement vs phase space (second law)

I've followed Leonard Susskinds series on "the theoretical minimum". In the entropy/reversibility episode in statistical mechanics, he explains (at least one way of) how the apparent paradox of ...
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### “Single-shot” Heat engine efficiency limits

The sun is 5778K and Earth is ~290K. Using the sun as the hot reservoir and earth as a cold reservoir we get 95% Carnot efficiency. However, the solar power efficiency limit is only 86%, see: http://...
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### Exhaust liquefaction in internal combustion engines

Does an internal combustion engine provide enough efficiency to still deliver mechanical power, if it is forced to liquify it's own exhaust gases by compression? If gas containers would be added to ...
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### Timescales of physical and chemical equilibrium

Background When describing the behaviour of a reacting systems, we usually don't hesitate to apply property models to relate the local properties of each species. For example, in the case of a gas ...
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### Volume Minimization Principle?

I know of two major extremum principles: Entropy Maximization: for a specified $(U,V)$, the equilibrium state has a higher $S$ than all non-equilibrium states, i.e., equilibrium occurs at the maximum ...
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### What is the best material to use in a solar heater box to convert solar energy into heat energy?

Suppose you want to design a solar heater box with the dimensions: 1 sq meter x 30.48 cm H. 5 sides of the box's interior will be insulated and the interior will be totally black. Ideal glass will be ...
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### How do I choose which thermodynamical potential to use to describe a phase transition?

While studying thermodynamics I came across the Gibbs free energy and the Helmholtz free energy... IF I understand thing correctly, when describing a phase transition I can use any thermodynamical ...
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### Le Chatelier's principle and energy minimization

In Callen's "Thermodynamics" in section 8.5 he asks us to imagine some perturbation $dX$ of an extensive parameter of a system in contact with a reservoir that acts to hold fixed the intensive ...
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### Do any substances have the same density when solid and liquid

I know that as you heat something it expands, but this is proportional to the change in temperature, so if I compare the density of a liquid right before freezing and right after then the thermal ...
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### Does second law of thermodynamics imply the big bang?

Given that the second law of thermodynamics states that entropy always increases and the universe is currently not in a state of maximal entropy does that not imply that it must have started at a ...
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### How to calculate the energy in thermoelastic damping?

Note - I'm not 100% sure *thermoelastic damping* is the right term here - so please feel free to correct the question in case I'm wrong! If a force is applied to an elastic rod such that it ...
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### What liquid would wick away heat most quickly?

I've read and seen on various "life hack" websites that if you've forgotten to chill drinks, wrapping them in a wet paper towel and sticking them in the freezer for a few minutes rapidly cools them ...
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### Why the non-analyticity of free energy function implies phase transition? And what's its connection with other 'higher level' free energies?

I have seen 'free energy' arising from several contexts in very different forms, and each contains different amount of information. For example free energy is defined as the logarithm of the ...
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### Is it possible to efficiently extract phonons from a lattice?

The population inversion generated in lasers occurs in multi-level atomic systems. As an example, the Nd:YAG energy diagram is shown below. The pump pushes the Nd ions up to the upper levels, and ...
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### Landau's derivation of the law of entropy increase - clarification

In Landau&Lifshitz V: Statistical Physics the following derivation of the law of increase of entropy is given. I need help understanding several crucial steps; I'll briefly summarize the notations ...
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### How much energy does it take to cook a steak?

Grilling in the park today I started to wonder just how implausible a portable battery-powered grill would be. There are of course a lot of parameters in this question, so let's narrow it down for now:...
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### Irreversible heat engines strictly less efficient than reversible ones

I understand how Carnot's theorem implies that irreversible heat engines must be no more efficient than reversible one's, but it is less clear why they need to be less efficient, as I have seen stated ...