# 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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### Isentropic or isenthalpic expansion for the remaining fluid in a previously pressurised tank?

Imagine a container filled with ammonia at 25 bar and 100 degC. Assume that an orifice is opened, so that fluid can flow through ...
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### Definition of heat from stat phys [duplicate]

I don't really understand how to couple the idea of entropy as info with heat. Let's say that you have an isolated system. A cube with a a series of movable partitions parallel to a face of the curve. ...
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### How can we calculate entropy produced by plastic deformation in this example?

Suppose we have a massless spring of spring constant $k$ attached to a mass $m$ at equilibrium position $x_{0}$ at temperature $T$. The mass may oscillate in one dimension only for simplicity. We ...
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### Confusion regarding the equation $dS=\frac{\delta Q_{rev}}{T}$

In Reif's Fundamentals of Statistical and Thermal Physics he outlines a "proof" (sections 3.8 and 3.9) of the equation $dS=\frac{\delta Q}{T}$ for any quasi-static, infinitesimal process (i....
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### Gravitational collapse - proof that energy dissipation is required?

As an undergraduate, I took a short course on astrophysics, where I encountered the Jeans mass. This is the critical mass for a spherical cloud of interstellar gas above which the cloud is predicted ...
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### Gibbs Free Energy and Definitions of Entropy [duplicate]

When we speak about entropy, it's classically defined as $\delta S = \frac {\delta Q}{T}$ Where, I emphasize that it's the definition for only a change in entropy and not entropy itself (That's how I ...
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### Different Bekenstein bound equations – what’s the difference?

Can someone help me understand the difference between the Beckenstein bound equations that I’ve come across? They all appear to have different dimensions. I’ve been told that if you include the ...
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### Why does entropy obey the superposition principle?

I was deriving the Boltzmann's entropy formula $${\displaystyle S=k_{\mathrm {B} }\ln \Omega}$$ We start with two prepositions: Let's consider two systems and we know the entropy of the first is $S_1$...
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### Definition of entropy and microstates (Huang)

The definition of Boltzmann entropy given in Ref. 1 appears to be different from most sources I've seen up to this moment. Let me start from the latter: typically textbooks assume that in a given ...
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### Does quantum entropy take into account the quantum uncertainties present in a system?

The von Neumann entropy of a mixed state is non-zero, and this makes sense as mixed states are just statistical descriptions of quantum systems, so there's some amount of classical uncertainty causing ...
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### Feasibility of entropy at zero temperature

I remember a college lecturer of mine once gave me this equation of entropy during one of his lectures on thermodynamics: \begin{align*} \Delta{S} = \frac{ d {Q} }{T} \\ \end{align*} I found out ...
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### How much information is encoded in a ball on a field? [closed]

Consider a soccer ball placed on a planar field of finite dimension (just like a soccer field). How much information can be realistically encoded in the position of the ball on the field?
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### At what size of matter does the second law of thermodynamics breakdown?

I'm in high school and I was studying some topics related to heat transfer. While studying, I was curious about why heat strictly flowed from a higher temperature (more energy) to a lower temperature (...
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### High fidelity implies low entropy

I was reading the security proof of QKD by Lo-Chau. One of their main idea is to bound the entropy of the eavesdropper if the singlet states are of high fidelity. Here I summarized the first lemma: ...
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### Is the 2nd law a reason for the irreversibility of natural processes or a consequence of it?

I have been introduced to chemical engineering thermodynamics due to my academic background. I had learnt about internal energy, entropy etc and applied the equations to various scenarios of practical ...
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### Entropy change of an isolated system consisting of two thermally conductive blocks of equal isochoric heat capacity at different temperatures

A classic example considered in most introductory treatments of elementary thermodynamics consists of two thermally conductive (e.g., metal) blocks placed in thermal contact. In particular, I find ...
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### Why must solids in equilibrium become crystalline?

In Landau's Statistical Physics's analysis of solids, he begins with the remark that solids are caracterized by their atoms' small oscillations about equilibrium positions. However, he states that ...
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### What exactly does the quantum mutual information measure? [duplicate]

Quantum mutual information (QMI) is often said to be the quantum mechanical analog of Shannon mutual information (MI). I realize they can be written with the same formula: $$S_x+S_y-S_{xy} \ ,$$ where ...
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### Unitary Evolution and the Second Law of Thermodynamics [duplicate]

Apologies for the long question. This problem has been mentioned multiple times on this platform, with no real resolution, in my opinion. So I'd like to gather all my thoughts below with hopes of ...
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### Is von Neumann entropy symmetric? [closed]

In a multiparty system, Shannon entropy is symmetric with respect to exchange of two parties. Is this also true for von Neumann entropy in case of a multiparty density matrix? If yes, is there any ...
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### Is it physically possible for an ordered system to endure forever? [duplicate]

I am seeking to understand whether my theological views align with the current understanding of the second law of thermodynamics. As a physicalist, I believe that all ontological existents consist of ...
1 vote
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### Meixner and the Impossibility of Non-equilibirum Entropy [closed]

Meixner in a series of publications, see a short list below, starting from 1959 criticized and ultimately denied the possibility of defining the entropy concept in an irreversible process. His ...
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### Entropy in irreversible adiabtic process

We know that, $$dS=\dfrac{\delta Q_{rev}}{T}$$ If you have an irreversible adiabatic process between two thermodynamic equilibrium end states of a system, there exists no possible reversible adiabatic ...
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### AdS$_3$ Geodesics' Length in ambient space as done in "Aspects of Holographic Entanglement Entropy"

I have been following the mentioned paper ("Aspects of Holographic Entanglement Entropy" hep-th/0605073 by Shinsei Ryu and Tadashi Takayanagi), trying to get into AdS/CFT. In section 6.2 ...
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### Why is entropy defined in the way it is?

In thermodynamics course we were taught that in a reversible adiabatic process of an ideal gas the entropy change is zero. Now what I didn't get intuitively is that if the system is compressed ...
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### Why is the number of microstates corresponding to a macrostate even finite for an ideal gas in a box? [duplicate]

I was looking at the Sackur-Tetrode equation which gives an exact formula for the entropy of an ideal gas. I tried to relate it to Boltzmann's famous $$S = k_B \ln(W)$$ where $S$ is the entropy and $W$...
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### Why does the entropy not decrease when inserting a partition into a macroscopic amount of different particles? [duplicate]

Here is a thought experiment. Imagine a box with 10^20 different particles, all different types of molecules, such that they are not indistinguishable according to QM. I insert a parition in the ...
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### Does temperature difference alone equate to stored energy?

A heat engine uses a temperature difference in a hot side and a cold side to produce work. But when you run a heat engine, with a fixed amount of heat in the hot and cold sides until equilibrium is ...
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### Partition function of $N$ distinguishable particles

Suppose there are $N$ distuinguishable particles. Each particle can have energy either $\epsilon_1$ or $\epsilon_2$. $n_1$ particles have energy $\epsilon_1$and $n_2$ particles have $\epsilon_2$ i....
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### Diffusion of van der waals gas

the problem is diffusion of non-ideal gas i think, in this situationm the change of internal energy, work, and heat during process is zero because this process is free expansion(diffusion) but, how ...