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 ...
Jean The Hedgehog's user avatar
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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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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 ...
spectralDecomposition's user avatar
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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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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 ...
Christoffer Corfield Aakre's user avatar
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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 ...
quantum rookie's user avatar
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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 ...
creillyucla's user avatar
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A case of limiting equilibrium

I have noticed in the solutions of the problems of Friction of a physics book I'm studying from that in cases of limiting equilibrium, the force of friction $f$ to be equal to the coefficient of ...
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Normalizability of thermal density matrix in QFT

Suppose that I have a system described by a quantum field theory with Hamiltonian $H$ and $U(1)$ charge $Q$. The thermal density matrix is then $$ \rho = \frac{1}{Z} e^{-(H-\mu Q)/T},\quad Z=Tr(e^{-(H-...
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Water equilibrium when relative humidity is high

Suppose a puddle has water and another component whose composition is known. The water in it would be in equilibrium with the water vapour following Raoult and Dalton's law (also here): $$P_T y=P^0_{...
BadEnglishSorry's user avatar
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Equilibrium points in lagrangian mechanics with generalized potentials

I understand the way i calculate equilibrium points when i have a lagrangian without mixed terms (with coordinates and velocities multiplied), thinking of the coordinate dependent part of the ...
forgetfuled's user avatar
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Doubts about direction of normal contact force acting on a tilted rod supported by another body

I'm confused about the direction of the normal contact force acting on a body supported by another body. I have read the following : If a body is being supported by a surface, the normal force acting ...
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Ergodic theorem with more conserved quantities

Ergodic theory is constructed by fixing the dynamics on a surface of the phase space with constant energy. In case a non-integrable system conserved more additional quantities apart from the energy, ...
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Are there methods to determine the equilibrium points of the general three bodies problem?

Starting from the three second-order differential equations, I have written the problem in the form of a system (from a modelling point of view): $$\mathbf{\dot{x}}=\mathbf{f(\mathbf{x})}$$ where $\...
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Under thermal equilibrium, spin stay still or oscillate?

Under thermal equilibrium, spin stay still or oscillate? For atoms with inertia, atoms will keep moving even the net forces are zero, they will oscillate with velocities. But spin does not have ...
高玉强's user avatar
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Necessary and Sufficient Conditions for an Equilibrium to be Stable

In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement: For the (mechanical) equilibrium to be stable, it is ...
Zephyr's user avatar
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Partition function for a system in local thermal equilibrium

For a system in equilibrium, the partition function is standard. But if the system is in local thermal equilibrium but stationary (i.e. zero or negligible time variation), but the temperature varies ...
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Calculate the average number of oscillators of an Einstein solid, in the grand canonical ensemble, when $q\gg N$

I am quoting from "Equilibrium and non-Equilibrium Statistical Thermodynamics", by M. Bellac. $$Q_{(\alpha, \beta)} = \sum_{N=0}^{\infty} e^{\alpha N} Z_{N}(\alpha, \beta) \hspace{1cm} (3....
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Bifurcation of Van Der Waal equation for real gases

Van Der Waal's equation leads to a cubic equation in v of the form $$Pv^3-(bP+RT)v^2+av-ab=0$$ This equation has 3 roots for $T<T_C$ and one root for $T>T_C$ I understand why region ABCDE is ...
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How does thermalisation make incoherent waves into coherent ones?

Thermalisation is the process by which out-of-equilibrium systems reach equilibrium. Coherence refers to the phases of waves being a constant difference apart. While reading a paper on axion stars, I ...
Nanashi No Gombe's user avatar
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3 answers
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Phase transitions and Helmholtz vs Gibbs Free Energy

Gibbs phase rule for Gibbs free energy says that phases during a phase transition must be in mechanical, chemical, and thermal equilibrium, e.g. $T_1=T_2$,$G_1=G_2$, and $P_1=P_2$, where the ...
mathdummy's user avatar
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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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Why dynamic equilibrium exists?

We know that at equilibrium Gibbs energy is minimum. We also know that at equilibrium both forward and reverse reactions occur simultaneously, and also we know that for a reaction to be spontaneous ...
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Vacancy Generation / Annihilation Time (Relaxation Time)

Vacancy Generation/Annihilation Time, Recombination Time and Relaxation Time ($\tau$) are all synonymously used in atomic physics literatures. They're defined as the time that it takes for vacancies ...
Ali Abbasinasab's user avatar
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Charge separation equilibrium equation for non-rotating blackhole at Eddington limit with spherically symmetric accretion?

What is the formula for equilibrium charge on a non-rotating black hole with spherically symmetric hydrogen-1 inflow at the Eddington limit of luminosity based on photon scattering acceleration of ...
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Container divided by frictionless adiabatic wall: reversible or irreversible process?

I have encountered an issue in the following physical situation. Consider a rigid, thermally insulated container divided by a barrier parallel to its base into two parts, left and right, each ...
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Show that equal pressure is the maximum entropy state

Some introduction and background Consider a thermally insulated reservoir filled with some gas. The reservoir is divided in two by a fixed, thermally conducting wall. Initially, the first compartment ...
Botond's user avatar
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1 vote
1 answer
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Calculate new equilibrium of cryogenic LNG tank after addition of new cold LNG

Disclaimer: I am not a physicist, but I am trying to unravel this problem and it is interesting me more and more the more I work and think about it. I have the following problem: There is a Cryogenic ...
wout konings's user avatar
1 vote
1 answer
45 views

Doubt on thermodynamics equilibrium

Is thermodynamics equilibrium related to mechanical equilibrium in anyway? For eg if the net Torque on a system is not zero does that still mean the system can be in thermodynamic equilibrium?
Iloveharmonics123's user avatar
1 vote
1 answer
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Deriving Non-linear acoustic wave models, equilibrium state assumption

The standard derivation in obtaining a single wave equation involves making use of the heat equation with a Taylor expansion of the equation of state, then differentiating this equation and the ...
sis's user avatar
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In a DC motor, why would the rotor oscillate around its stable equilibrium point, had there been a constant current?

If I choose to replace the commutator in the motor with two slip rigs like those in the AC dynamo, then when the plane of the motor is normal to the magnetic field, aligning, therefore, the magnetic ...
Jack's user avatar
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Phase Equilibrium Conditions

In explaining phase equilibrium, my textbook gives an example of two phases ($\alpha$ and $\beta$) of the same species coexisting together and isolated from the rest of the world. With the total ...
Abe 's user avatar
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1 vote
3 answers
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Inelastic static tetrahedron with 3 fixed vertices, and 1 free vertex with an applied force

This is a problem I've posed myself, which I cannot for the life of me figure out, despite it clearly having a definite answer. Given: A perfectly inelastic tetrahedron in three-dimensional space ...
Silas Hokanson's user avatar
1 vote
1 answer
455 views

If three forces act on an object in equilibrium, they must pass through a common point. How does this generalise?

If three forces act on an object in rotational equilibrium, the line of action of each force must pass through a common point (parallel forces satisfy this as they go through a common point at ...
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Time-Independent Quantum Hamiltonians and Thermodynamic Equilibrium

Suppose we have a time-independent Hamiltonian operator $\hat{H}$ of some system. We know that we can express the canonical partition function of said system as $z = \text{Tr}(e^{\beta\hat{H}})$ for ...
Jepsilon's user avatar
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Terminology for scenario when energy of system $E(\theta_1,\ldots,\theta_k)$ with $k$ real parameters, is minimum whenever $\theta_1=c$ (fixed value)

Disclaimer. I'm not a physicist. Consider a physical system whose "energy" $E$ is a function of $k$ real parameters $\theta = (\theta_1,\ldots,\theta_k) \in \mathbb R^k$. Let $E_{\min}$ be ...
dohmatob's user avatar
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Can someone explain Couple with respect to forces acting on it?

Suppose two inequal, parallel and opposite forces $P$ and $Q$ are acting on a body not along the same line, producing a clockwise moment. If the rod on which its acting is massless, then we can extend ...
AltercatingCurrent's user avatar
1 vote
2 answers
140 views

Statics question: Free body diagram help for garage construction project

I'm building a climbing training apparatus in my garage that both rests on the ground and hangs by a rope from a hook attached to a ceiling joist. Here are some pictures of builds similar to what I'm ...
Wilder Boyden's user avatar
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A comparative study between individual blocks to one long block

In relation to two previous discussions about Newtonian mechanics first asked by esdoublef Free body diagram on a rack of wooden blocks and afterwards silverrahul, Horizontal Rack of blocks revisited ...
Kenji Chng's user avatar
1 vote
1 answer
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Balance of an non-homogeneous object

Would a pencil balanced on its tip, remain balanced if the the tip was made of a material twice as heavy than the rest of the pencil?
eliza blok's user avatar
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Minimum energy principle for stars

In Townsend's Black Hole lecture notes, he says that at equilibrium, $E = E_{grav} + E_{kin}$ is a minimum, where $E_{grav}$ is the gravitational potential energy $-\frac{GM^2}{R}$ and $$E_{kin} = nR^...
DentPanic42's user avatar
1 vote
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Find minimum radius of an asteroid before it becomes round using bulk modulus and hydrostatic equilibrium

How big must an asteroid be before gravity makes it round and hydrostatic equilibrium comes into the equation? Let's say that being a round planet requires a radius error of $\frac{\delta R}{R}$ that ...
alwaysq2000's user avatar