# Tagged Questions

The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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### What is the black hole information paradox really?

Preliminaries What is the black hole information paradox really? Is it a sophisticated way to ponder and debate the existence of an operator on the boundary that can tease out the interior of a ...
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### Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
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### Entropy of the cosmological constant and the laws of thermodynamics?

Convention The convention being used is: $A_{C} =$ The classical variable Premise Consider the following toy-model universe: A universe with a positive cosmological constant. Basic ...
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### Is there a block spin renormalization group scheme that preserves Kramers-Wannier duality?

Block spin renormalization group (RG) (or real space RG) is an approach to studying statistical mechanics models of spins on the lattice. In particular, I am interested in the 2D square lattice model ...
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### Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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### Video lectures for studying graduate level kinetic theory

As the title says it all, I require Video lectures for studying graduate level kinetic theory including but not limited to detailed analysis of viscosity and conductivity, diffusion and Maxwell's ...
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### How to explain the Venturi effect with Kinetic Theory?

From a macroscopic perspective a fluid flowing through a pipe gets accelerated when the pipe's cross section gets narrower. According to $F= ma$ a force must be present to do this. This force is ...
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The imagined scenario: Part A: From special relativity we know that velocity is a relative physical quantity, that is, it is dependent on the frame of reference of choice. This means that kinetic ...
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### Books on entropy [on hold]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
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### Specific heat of water

In statistical mechanics, we derive all the thermodynamic quantities, including specific heat $c_v$ from the partition function $Z = \mathrm{Tr} \, [ \, e^{\beta H } \,]$ . For solid, we assume simple ...
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### Canonical ensemble: correlation function for quadratic potential energy

In this paper I can't understand the following A given system has the potential energy $U(x_1,x_2,x_3)=k_1 x_1^2 + k_2 (x_2-x_1)^2 + k_3 x_3^2$. Since the energy is quadratic, the correlation ...
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### Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
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### ploting probability distribution of energy in Canonical ansambel [on hold]

To reproducing fig3.3 statistical mechanics pathria, probability density function of energy: $$p(E)\quad \alpha \quad e^{-\beta E} g(E) = e^{-\beta (U-TS)}~ exp{(-\frac{(E-U)^2}{2KT^2C_V})}$$ . I ...
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### Canonical partition function and counting

That's a silly silly question, so my apologies, but in this moment I could not reach out! Let's have a system made of a particle reservoir $R$, and a subsystem $S$. The total particle number is $N$. ...
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### If I prepare a state (density matrix) in Gibbs state, does it go to the lowest energy state at very low temperature?

Gibbs state is $$\rho_G=\frac{1}{Z} e^{-H/kT} = \sum_n \frac{1}{Z} e^{-E_n/kT}|E_n⟩⟨E_n| \, .$$ If $T$ goes to zero, does it mean the $\rho_G$ goes to the lowest energy state $|E_0⟩⟨E_0|$?
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### How to prove that Gibbs state remains a gibbs state after evolution?

Gibbs state is $$\rho_G=\frac 1Z e^{-H/kT}=\sum_n \frac 1Z e^{-E_n/kT}|E_n⟩⟨E_n|.$$. In wikipedia, it is said that a Gibbs state is an equilibrium probability distribution which remains invariant ...
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### Two conflicting forms of equation of state of non-relativistic gas

I've run into two conflicting derivations of the equation of state of a non-relativistic gas. However, the derivations of the relativistic equation of state of both sources agree. I think maybe the ...
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### Why Doesn't Einstein Get More Credit for Being the Father of Quantum Theory? [on hold]

I'm not simply referring to the notion that Einstein treated the discrete emission and transference of energy (and matter) as "real" physical phenomena, but rather his major continuous role in the ...
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### Moment direction and force [on hold]

Replace the three forces acting on the plate by a wrench. Specify the magnitude of the force and couple moment for the wrench and the point P(x, y )where its line of action intersects the plate. FR=...
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### Volume Operator / volume phase-space-function in thermodynamics

In Thermodynamics, one often encounters the derivation of pressure as the generalised force that belongs to the extensive state-variable of the volume. Postulates: One looks just at a system of many ...
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### Overcounting and what is indistinguishable about indistinguishable particles?

When getting the overcounting factor in statistical mechanics, how does one compute it? Let's say each property is unique in one aspect (a string with an unique address in pc memory for example). ...
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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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### Chemical Potential as a function of Temperature

I have considered an ideal fermi gas. Then, we can obtain an expression for chemical potential as a function of Temperature. I want to understand the physical significance to it or what it really ...
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### Mixed Gas Absorbtion

Consider a gas misture that contains two type of atom, A and B. The gas is in equilibrium at temperature $T$. If on the surface of the gas container there are M sites that can absorb an atom gas, and ...
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### Does a theory exist with a symmetry between a tachyonic and non-tachyonic mass points which preserves the normal laws of the mechanic?

Does a theory exist with a symmetry, which mirrors the tachyon mass points to non-tachyon mass points and vice versa? I think, it would be very beautiful, despite that there are strong theoretical ...
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### What does $f(v)d^3v$ mean?

I am reading the derivation of Langmuir's Evaporation Equation. The author writes: That cylinder contains a volume $dA(vdt)cosθ$ and contains vapor molecules of the designated speed in the ...