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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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Correlated quantum systems

I am working on correlation in quantum systems and would like your comments regarding correlation in quantum systems and to fill the gap in the proofs or to use another type of such relations with the ...
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Trying to understand entropy as a novice in thermodynamics

I recently had my second lecture in Thermodynamics, a long lecture which involved the first law and a portion of the second law. At some point during the lecture we defined entropy as the change of ...
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1answer
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What is the information concept and how can it be measured,…?

According to the Wikipedia, ""Information of an entity is that which resolves the uncertainty of its properties"" source: Wikipedia, physical information Information contained in a physical ...
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Entropy and temperature of small systems

I've been struggling for a while now in understanding the concept of entropy as a function of the internal energy. Textbooks typically call $g(E)$ the number of microstates compatible with an energy $...
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1answer
56 views

Why is the energy able to be supplied by the environment equal to TS and not something much more complicated?

In Daniel Schroeder's book Thermal Physics, he discusses the amount of energy needed to create an object, or its internal energy. He makes the point that you don't need to supply the entire energy U, ...
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1answer
45 views

Why is the thermodynamic definition of temperature only valid for large systems?

I remember my thermal physics instructor telling me that the definition of temperature, $$\frac{1}{T} \equiv \left(\frac{\partial S}{\partial U}\right)_{N, V},$$ is only valid for (sufficiently) large ...
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49 views

$N$ Independent Oscillators Entropy and Number of States

I have been working on building intuition and experience with solving problems related to the microcanonical ensemble, but I haven't been able to solve the following problem: If you have $N$ ...
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24 views

Microcanonical Ensemble Entropy of System with Degeneracy

So, I have been trying to find the entropy of the following system as a function of energy: the system consists of N atoms, N much greater than 1. Each atom has three energy levels: the ground state ...
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41 views

Can two quasi-static adiabates intersect? [closed]

I saw a question in my physics book that I've been trying to understand lately. The question is simple: given two quasi-static adiabatic curves, could you find a point of their intersection? Also, ...
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Proving that $dS$ is an exact differential mathematically

OK...so I hope this is not too dumb a question: We know that we can express $dS$ as $$dS=\frac{dQ}{T}=\frac{C_v}{T}dT+\frac{R}{V}dV,$$ where $C_v$ is the thermal capacity at constant volume and $R$ ...
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I'm confused to understand von Neumann entropy and purification [closed]

In my textbook, for all density matrices, von Neumann entropy has the following properties: (1)$\forall \rho \in S(\mathbb{H}), H(\rho )\ge 0$ and $H(\rho )=0 \iff \rho$:pure state (2)$\forall \rho _1,...
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What force causes entropy to increase?

What force causes entropy to increase? I realize that the second law of thermodynamics requires the entropy of a system to increase over time. For example, gas stored in a canister, if opened ...
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What's the Entropy change in Quantum Teleportation?

Suppose a single qubit quantum teleportation From A to B through a bell states by quantum gate performance. The setting was the usual one usual one i.e. Suppose initial the unknown states $|\psi\...
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3answers
34 views

How does a bottle filled with fluid which has been vigorously shaken, lose entropy to the surroundings?

Suppose a bottle is filled with a hypothetical liquid that cannot absorb air/gas. The cap is tightened enough to prevent any loss or gain of mass. Now, this bottle is vigorously shaken and then ...
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State typicality/describability as a model for entropy?

I've heard of the metaphor of a finite 2D square grid with each square in one of two states as being (sufficiently in this case) like a universe, or large piece of the universe. Most of the states in ...
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1answer
25 views

Change of entropy of mixing in terms mass ratio

I am stuck on this problem. Suppose we are mixing substances $a$ and $b$, we have $$\Delta S_{mixing} = -Rn_a \ln (\frac{n_a}{n_a + n_b})-Rn_b \ln (\frac{n_b}{n_a + n_b})$$ and we are told to ...
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1answer
24 views

Entropy of a system of black balls and white balls. The black balls are heavier

Let's say I have a Jar filled with equal amounts of black balls and white balls that are the same shape and size. The position of each ball in the jar is a random coordinate. Completely arbitrary. ...
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Matching the accessible phase volume of an ideal gas to Boltzmann's equation

I have been attempting to calculate the entropy increase of a monatomic ideal gas upon addition of a small amount of heat, and have been unable to resolve an apparent contradiction between the ...
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3answers
99 views

How can temperature be defined as it is if entropy isn't a function of energy?

I've been taught that for large systems, the temperature of a system is defined as $$\frac{1}{T} \equiv \left(\frac{\partial S}{\partial U}\right)_{N, V}.$$ I have a problem with this definition, ...
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3answers
53 views

Reversible reaction for Entropy Change of Surroundings

When learning about Entropy in my introductory lecture, I learnt that in basic terms, entropy can be spoken about as $$dS = \frac{dq_{rev}}{T}$$ and the lecturer mentioned that as Entropy $S$ and $T$...
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3answers
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Ambiguity in the definition of entropy

The entropy $S$ of a system is defined as $$S = k\ln \Omega.$$ What precisely is $\Omega$? It refers to "the number of microstates" of the system, but is this the number of all accessible microstates ...
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1answer
40 views

Definition of entropy for canonical vs. microcanonical ensembles

The two following definitions of entropy are often used in the microcanonical and canonical ensembles, respectively: $S=k_b\ln(\Omega)$ $S=-k_b\sum_ip_i\ln(p_i)$ I am curious how the second can be ...
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Confusion regarding indistinguishability of particles and the definition of Gibbs entropy

I have been reading about the Gibbs paradox, in which the assumption that particles of a monoatomic ideal gas are distinguishable leads to a paradox in which entropy is not extensive. In Schroeder's ...
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Entropy derivation question

I’m using Atkins thermodynamics book and he has a section I don’t quite understand. The line I’m particuarly question is the one befor (5.2) where he says “by Kelvins formulation of the second law”. I’...
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About the von Neumann entropy after the partial trace

In the quantum information field, it is widely known that the von Neumann entropy of a state $\rho$ is 0 if and only if $\rho$ is a pure state. If we restrict the state as a pure entangled state, is ...
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1answer
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Why does entropy of an ideal gas break the third law of thermodynamics? [duplicate]

I was recently looking at the entropy equation for an ideal gas, show below $$S=NR\left\{\frac{5}{2}+\ln\left[\frac{V}{N}\left(\frac{2\pi mRT}{h^2}\right)^{3/2}\right]\right\}$$ And what troubles me ...
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The Borel Argument - 1 cm displacement of hydrogen atom on distant star effect on microstates on system on Earth

I was wondering if anyone had the derivation to Borel's famous arguement that a displacement of 1 cm on a particle on a distant star would significantly affect the microstate configuration on a system ...
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68 views

Meaning of zero temperature in terms of $1/T=\partial S/\partial E$

Suppose we have a $NVE$ system of a pure crystal. From the definition of the temperature in macroscopic thermodynamics, $$\frac{1}{T}=\left. \frac{\partial S}{\partial E}\right |_{V,N}$$ . Then ...
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3answers
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How does $dS \ge 0$ imply a system cannot receive more energy than work supplied?

I am reading a book that asserts the following: The second law arises from an equation of the form $$dS = \mu\,dE + \mu\,dW \tag{1}$$ where $dS$ is the change in entropy, $dE$ the change ...
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1answer
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Could micro-states not have equal probability as assumed? [closed]

How could micro-states have uniform distribution in a 3D space unless there was 0 Gravity? Gravity violates the assumption of equal probability as it makes matter move in a predictable direction. ...
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As the universe expands, ultimately, will it continue to reach closer and closer, to absolute zero but never get there?

First law of thermodynamics, the conservation of energy, doesn't this law all but guarantee that regardless of how far the universe expands it will forever contain its original amount of energy? All ...
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4answers
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Why does energy flow downhill/entropy increase?

I'm not sure if this is asked anywhere else before, but so far my search isn't fruitful. I'm in my second bachelor of physics and mathematics, and currently taking a thermodynamics course. We just ...
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1answer
40 views

Confusion about microstate probabilities

So I know we have the Gibbs Entropy Formula $$S=k\sum_i p_i \ln p_i$$ And I've seen the probabilities for the microstates be said to be the Boltzmann probabilities $$p_i\propto e^{-\frac{E_i}{kT}}$$ ...
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2answers
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Confusion with Entropy [closed]

If a system spontaneously expands it should also increase in entropy by the second law of Thermodynamics. But we know that gases cool when they expand, not heat up. How can $CdT$ be negative and $TdS$ ...
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Entropy due to iron block on the universe? [closed]

Suppose we have two objects made of iron, one hot the other colder. What happens to the entropy of universe when we bring them in contact, will it increase or decrease? Why? How can we prove that ...
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How to calculate the logarithm of an outer product?

Im tryting to calculate the entanglement entropy of a subsystem: $$S_\text{ent}=-k\cdot \mathrm{Tr}(\rho_A\log(\rho_A))$$ Let $$ \rho_A=\vert\uparrow\rangle\langle\uparrow\vert$$ from what I can ...
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How does a microcanonical ensemble maximize entropy?

A microcanonical ensemble is one that represents an isolated system with fixed number of particles, volume, and energy. In other words, it's an $(N,V,E)$ ensemble. If the energy is fixed, it will ...
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Deriving the ideal gas law from relative entropy, instead of differential entropy, to avoid negative entropy

Deriving the ideal gas law is one of the first examples presented in introductory statistical physics. It is derived using the differential entropy. Let $\chi$ be an uncountable set. Then the ...
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1answer
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Specific entropy of dry air formula?

I work with one old report and I need to convert their calculations to the SI units. They calculate the specific entropy of the dry air there this way: So I need to decide what to use instead of R ...
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3answers
136 views

Why the entropy change is not zero in the irreversible adiabatic process?

Why the entropy change is not zero in the irreversible adiabatic process? while it is defined as the integral of the heat added to the system over its temperature
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1answer
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Non-Isentropic Turbine

comparing to an Isentropic turbine I was wondering if you could help me answer a question I coulnd't find the answer to. If I have a non Isentropic Turbine... why doesn't the pressure difference ...
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5answers
197 views

Concerning heat engines and entropy

In deriving the inequality $$e \leqslant 1 - \frac{T_c}{T_h},$$ Schroeder, in An Introduction to Thermal Physics, uses the fact that for one complete cycle of a heat engine, $$\frac{Q_c}{T_c} - \frac{...
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25 views

Confusion on Carlip's approach to Cardy Formula

I'm reading Carlip's approach to Cardy Formula (https://arxiv.org/abs/hep-th/9806026). He considers the partition function on the torus of modulus $\tau$ to be $$\mathcal{Z}(\tau, \bar{\tau})= \text{...
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1answer
58 views

An issue with thermodynamic properties of infinite systems

I have the following problem. Given a finite system, let us say a box of side $L$ containing $N$ "ideal gas" non-interacting particles, properties such as the entropy can be defined, in this case, $S ...
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685 views

Are Mirrored Universes With Opposing Directions of Time Theoretically possible? [closed]

I found an article that talks about this here, entitled "Big Bang May Have Created a Mirror Universe Where Time Runs Backwards". I know any notion of backwards time is probably a dead horse in this ...
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1answer
42 views

Physics of time running backwards

Although it would seem weird to analyze physical phenomena when time runs backwards, it seems to have a logical sense, at least for me: Entropy would tend to decrease: two balls having energy ...
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77 views

How do we quantify and measure the net entropy of today's universe?

We know that the Universe evolved from a very low entropy state in the early universe to very high entropy state of today's universe. What is the quantitative definition of the net entropy of the ...
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1answer
68 views

Question on Partial Differentiation in Thermodynamics

For energetic fundamental relation $U=U(S,X_1,\ldots)$ where $X_k$ represent extensive parameters $V$ or $N_j$, let \begin{equation}P_k=\frac{\partial U}{\partial X_k}.\end{equation} For entropic ...
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1answer
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What does it mean for thermodynamic entropy to be defined only up to a constant?

I'm reading the Wikipedia article on thermodynamic definition of entropy. Because the energy of a particle in a classical thermodynamic system is a continuous variable, the number possible states is ...
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How looks the “overarching” wavefunction of a number of electrons in an insulating sphere?

I changed my question after reading the comment of Anna. If we put a huge number of electrons inside a non-conducting sphere, what will the total wavefunction describing all electrons look like? I ...