Questions tagged [equilibrium]
Equilibrium is the condition of a system in which all competing influences are balanced. These can range from forces (static/dynamic equilibrium), to chemical processes (chemical equilibrium) and temperature gradients (thermal equilibrium).
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Entropy and equilibrium concepts at astronomic scales
I am always puzzled to read here and there discussions dealing with thermodynamic concepts applied to astronomic scales where gravity matters. To my opinion, there is a certain carelessness to go into ...
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Demonstration that electric current at equilibrium is zero in crystals
As it is well known, electrons at equilibrium (no external field) do not conduct electric current, i.e.
$\int_{BZ} dk\,v_{k}\,f(\epsilon_k)=0$
where $f(\epsilon_k)$ is the Fermi-Dirac distribution
$...
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Can a substance have zero vapour pressure above absolute zero?
According to this Reddit thread, the answer is no, vapor pressure can't be zero when temperature is above absolute zero. I suspect the answer might actually be yes according to a precise definition I ...
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Empirical equivalence of shifted chemical potential $\mu_i$
It is often said that, in classical thermodynamics, entropy $S$ and energy $U$ are defined only up to an additive constant proportional to the total amount of substance $N=\sum_i N_i$ (where the sum ...
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Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum
Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...
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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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What are the maximum spring lengths of a double spring pendulum?
NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram
For a single spring, you can simply equate ...
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What are some good articles on trend to equilibrium?
I am interested in studying systems out of equilibrium that are trending to equilibrium. Trend to equilibrium, entropy production, etc. seem to be very tricky topics. Any suggestions will be ...
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Is there any example of a real-life system which violates the "third law" of thermodynamics while remaining at equilibrium?
I assume the following statement for the "third law" of thermodynamics:
$$\lim_{N \to \infty} \lim_{T \to 0} \frac{S}{N} = 0 \tag{1}\label{1}$$
That is to say, I am considering those systems with a ...
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Terminology of different equilibria?
I've heard many equilibrium terms:
Translational equilibrium
Rotational equilibrium
Static equilibrium
Dynamic equilibrium
The different terminology is slightly confusing. My understanding is as ...
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Quantum Hall Effect: Two-terminal resistance and thermodynamic equilibrium
In Goerbig's lecture notes on the quantum hall effect, Fig. 3.3 describes the so-called two-terminal measurement. The figure and accompanying text show us that in a two-terminal measurement, the ...
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Do all gravitationally collapsing objects virialize?
For interactions via a Newtonian gravitational potential, the virial theorem states that
$$ 2 \langle T \rangle = -\langle V \rangle $$
i.e. the time-averaged total kinetic energy and total potential ...
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Does Heat Equation really describe thermodynamic temperature?
We learnt that in the first PDE course, temperature profile could be described by heat equation.
\begin{align}
\frac{\partial{u}}{\partial t} \;=\; \alpha \nabla^{2}u \tag{1} \label{heat-eqn}
\end{...
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Is there an open quantum system analogue of the equilibration time bounds for classical ergodic Markov chains?
Background
For classical ergodic discrete Markov chains, we can bound the time taken to reach the stationary distribution to the spectral properties of the transition matrix. I will outline this ...
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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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