Questions tagged [entropy]

An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

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Thermodynamic entropy vs statistical mechanical entropy

In thermodynamics, we define the change in entropy of a system as: where $T_b$ is the temperature at the boundary of the system. But in statistical mechanics, we define the change in entropy of a ...
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Will the calculated mathematical probability of a decrease of disorder in mixing of gases violate the second law of thermodynamics?

I have read that two different gases mix together when the separation between their chambers is open so as to increase entropy.Similarly the mixed gases won't separate by itself so as to not decrease ...
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Using quasistatic processes to calculate quantities

This question is inspired by Reif Problem 5.5. Note that it is not a homework problem and, even if it were, my question only loosely relates to it. A vertical cylinder contains $N$ molecules of a ...
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What is the meaning of mutual quantum information?

I'm having some difficulty understanding the physical meaning of the mutual information that two subsystems share with each other. For example, if $\rho_{AB}$ defines the matrix of a bipartite state, ...
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How do I calculate enthalpy and entropy from Gibbs energy? [closed]

If for a system the Gibbs energy depends on the temperature like this: $$G(T) = aT + b + c/T$$, how would enthalpy and entropy depend on temperature?
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Boltzmann vs Gibbs definition of entropy [duplicate]

I am learning Statistical Mechanics and I have a question regarding different definitions of (statistical) entropy. If we use Boltzmann's definition: $$\sigma \propto\ln(W)$$ Where $\sigma$ is the ...
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What are the applications of materials if their entropy increases with temperature? [closed]

What could be the possible applications of the materials if their entropy increases with increasing temperature.
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To clarify the entropy/ energy/ Gibbs Eqs

Both case are isothermal and internally reversible processes. Why is it wrong to use energy conservation in case7-24 to solve the problem? I referred to the textbook (Aqueous tea An Engineering ...
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How to derive Shannon Entropy from Clausius Theorem?

I am studying Quantum Information now, and I need to understand the entropy of a quantum system. But before I go there, I need to understand Shannon Entropy which is defined as : $H(X) = -\sum_{i=1}^{...
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Conformal Cyclic Cosmology

In this conformal cyclic cosmology, where did the very first eon come from? How did the very first eon start with possible lowest entropy?
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"Universal" versus "nonuniversal" in the topological entanglement entropy

In their seminal paper, Kitaev and Preskill consider a 2D area law for entanglement of the form $$ S(\rho) = \alpha |\partial A| - \gamma + \cdots. $$ Here $\rho$ denotes the density matrix associated ...
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What does length dependent entropy means?

I've this problem from homework sheet, which asks to write down the L-dependent part of the entropy. I've no idea what does it mean? The Hamiltonian of the system is defined as $$ \mathcal{H}(p_{i}, ...
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String theory hilbert space - Gas of free gravitons

I am trying to understand the arguments given in MAGOO in chapter 3.4.1(Hilbert Space of String Theory). The authors give descriptions of the Hilbert space of String Theory when we consider our theory ...
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Is incompressible fluid flow isentropic?

I was asked to verify the relation $\partial_t(\nabla \times v)=\nabla \times (v \times (\nabla \times v))$ of an incompressible fluid flow, where $v$ is the flow velocity. I was looking at Landau and ...
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Why is it so much harder to keep the same room cool than to keep it warm?

I have read this question: Let me offer a different perspective on this. Cooling is not universally harder than heating. Why is cooling much harder than heating? Now I have noticed that whenever in ...
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What is the measure of decoherence?

Assume we have a qubit, and it is interacting with the environment. I know that people say that when the qubit is in $$\begin{pmatrix}\frac{1}{2}&\frac{1}{2}\\ \frac{1}{2}&\frac{1}{2} \end{...
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How can we prove each energy in different condition become minimum when thermal equilibrium

My question is like the title. We know in condition : const volume, entropy -> internal energy(U) reach minimum when thermal equilibrium. condition : const pressure, entropy -> enthalpy(H) ...
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Slope of constant pressure line on $T$-$S$ plot

Is slope of constant pressure line is same or di in liquid region and super heated region for pure substance on $T$-$S$ diagram?
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How is the Big Bang compatible with the preservation of quantum information?

As detailed at https://en.wikipedia.org/wiki/No-hiding_theorem , in the quantum world, information cannot be created or destroyed. The Bekenstein bound limits the amount of information that can be ...
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Is 'heat has only sources, no sinks' an equivalent formulation of the second law?

I was thinking about it and in a sense heat is an interesting quantity that can only be created and not destroyed. In comparison with the first law this means that ultimately for a closed system all ...
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Why does a null entropy variation along a closed timelike curve imply a reversible process?

Carlo Rovelli in one of his articles from 2019 (reference: https://arxiv.org/abs/1912.04702) argues that time travel into the past are thermodynamically impossible: For instance, if we want to travel ...
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Is $\frac{\Delta Q}{\Delta S} = T $ a meaningful equation and what would it actually represent?

The following equation gives the relation between entropy, heat and temperature: $$ \frac{\Delta Q}{T} = \Delta S $$ So when you add a certain heat at a certain temperature, you increase the entropy ...
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Entropy and resonance

I'm interested in determining whether the entropy of a vibrating string fixed at two ends can be expressed as a function of frequency. Particularly, the entropy at resonant frequencies. I'm not sure ...
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What stops entropy from forming if you extract 100% of heat flow and use it for work?

In a carnot engine you convert 100% of heat put inside the system during the isothermal phase into work. This is the basis of maximum efficiency and makes sure that it is reversible. If you don't ...
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The entropy given by stefan Boltzmann's law looks remarkably similar to the volume of the sphere; $S(T)=\frac{4}{3}\sigma T^3$

If I am not mistaken the entropy for a blackbody per unit area is given by: $$S(T)=\frac{4}{3}\sigma T^3.$$ The volume of a sphere is given by: $$ V(r) =\frac{4}{3}\pi r^3. $$ Is this coincidental? I ...
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Why an energy constraint gives the canonical ensemble (NVT) when we maximize von Neumann entropy, when energy is not conserved in NVT?

In Sakurai and Napolitano's Modern Quantum Mechanics 2nd Edition, I'm learning Section 3.4, page 188 where they derive the canonical ensemble by maximizing von Neumann entropy with energy constraint. ...
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Equivalent Formulation of Least Squares Method in Terms of Entropy

I have learned that people in the field of machine learning and statistics often use the least squares method. Is there any alternative formulation of the least squares method using entropy? (It might ...
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Finding equation of internal energy in adiabatic process

I am doing a review of thermodynamic and I encounter the following question, Show that if a single-component system is such that $PV^k$ is constant in an adiabatic process (k is a positive constant) ...
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What is the type of system, if I have an opened container with hot water inside, but no heat input to the system?

I have a school project, where I am trying to generate electricity using TEG modules that are attached to an aluminium container that contains hot water. The container is opened and there is no heat ...
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What's the definition of temperature ? What's the meaning of reaching a zero temperature and infinity temperature? [duplicate]

I'm taking a course about statistical mechanics and it is completely new to me . We've learned about entropy and how when 2 different sub-systems comes to contact the entropy of the whole system keeps ...
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Is there a clear analogy here between volume and entropy? Looking at: $ \frac{dQ}{T} = dS, \frac{dW}{P} = dV$

The first law of thermodynamics states: $$ dE = TdS + PdV $$ And entropy is defined as: $$ \int \frac{dQ}{T} = S \qquad(1)$$ If we make an analogous relation using the second term in the first law, ...
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Calculate the entropy for an arrangement of quantum particles

I am not a physicist, just read some pages of information theory, and wondered how far off this idea is: Imagine 2 levels and 3 particles that can be distributed in those levels. Also, each state-...
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How to find a complete understanding the 2nd law of Thermodynamics in terms of forms?

I have two straightforward question, and below I introduce more context to interpret them: What is, or is there, an order relation for forms that one can use to make sense of the 2nd law of ...
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What does "energetically favorable" mean?

Does it mean that the reaction is exothermic? Or does it mean that $\Delta G<0$?
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Derivation of entropy, I don't understand the relation $ \frac{\partial S_2}{\partial E_1} = -\frac{\partial S_2}{\partial E_2} $

My course guide gives the following derivation for change in entropy w.r.t. energy, where I don't understand a step: \begin{align} E & = E_1 + E_2 \\ S & = S_1 + S_2 \\ S(E,E_1 ) & = S_1 (...
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What is entropy in the concept of arrow of time? [duplicate]

When I first started to study arrow of time, I first heard the word Entropy and after watching and reading internet resources I can't get what is this in the concept of arrow of time. So, please tell ...
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Mixing identical gases in different states (Gibbs paradox)

Background It is well known that if we take a container separated into two volumes $V_1$ and $V_2$ by an insulating membrane and containing some moles $n_1$ and $n_2$ of the same gas at the same ...
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What's the variation of entropy of an irreversible process?

I'm studying entropy, in particular the increase of entropy principle, and I have a doubt about the entropy variation of an irreversible transformation. If I have two thermodynamic states, A and B, ...
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Do black hole horizons always increase?

In asymptotically flat spacetimes, the area of a black hole event horizon must always increase, provided the Null Convergence Condition is followed ($R_{\mu\nu}k^{\mu}k^{\nu}\geq0$ for all null ...
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How does the physics definition of a non-spontaneous process not violate logic? [closed]

The Second Law of Thermodynamics and The Law of Excluded Middle (The Definition of 'Non-Spontaneous' in Physics vs. in Logic) A thermodynamic process can only belong to one of the following options: ...
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Memory effects in clopen quantum systems

A clopen quantum system may be defined as one where there is no global dissipation (e.g. a finite system of interacting spins without photonic coupling.) In the open quantum physics literature, it is ...
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Entropy Calculation from Regularized Hamiltonian

I refer to Srednicki's 'Entropy and Area' paper here.I want to derive the expression for entropy (20), given by $$S_{l}(n,N) = \xi_{l}(n)[-\log\xi_{l}(n) + 1], \xi_{l}(n) = \frac{n(n+1)(2n+1)^{2}}{64l^...
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Thermodynamic potentials and Entropy [duplicate]

Is there a more intuitive way to explain the thermodynamic potentials, $G$ (Gibbs free energy) and $H$ (Helmholtz free energy). I think the major problem having with the explanations is because i need ...
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How to Understand the First Term in the Calabrese-Lefevre Distribution?

I am currently reading the following paper and I am trying to understand the first term in equation (6) (reproduced below): $$ P(\lambda) = \delta(\lambda_\text{max} - \lambda) + \frac{b \Theta(\...
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Technical review article on black hole thermodynamics?

Can anyone recommend a resource on black hole thermodynamics for physicists who are not familiar with this area? I'd like to see a rough sketch of the derivations of black hole entropy and Hawking ...
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How is entropy a state variable, and how can we measure entropy from irreversible processes with reversible ones, from a Khan Academy video

My questions : How is entropy a state variable? Why can we use a reversible process to measure an irreversible process's change in entropy if irreversible processes generate extra (unaccounted for ...
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How to Prove A Claim made to Construct the Calabrese-Lefevre Distribution?

My question is a mathematical one based on this physics paper. Suppose that $\lambda_i $ is an eigenvalue of a reduced density matrix. Up to a normalization factor, the distribution of eigenvalues is ...
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Efficiency of heat exchanger

During the practical work we were studying singular, multibular and plate heat exchangers, for all of them we got efficiency more than 100%, is it possible or what affects to efficiency? We calculated ...
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Is there a quantum of entropy - and how large is it?

Google Scholar lists quite a number of papers when searching for "Quantum of entropy" or "entropy quantization". Most are old. Some of these papers mention k as quantum of entropy, ...
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Is the statement $dF=(\delta Q-TdS)-pdV-SdT$ more general than $dF=-SdT-pdV$?

So the Helmholtz free energy is defined as $F=U-TS$, which means $$dF=\delta U-TdS-SdT$$ $$=(\delta Q-pdV)-TdS-SdT$$ $$=(\delta Q-TdS)-pdV-SdT.$$ since $\delta Q \neq TdS$ ($dS \geq \delta Q/T$) in ...
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