A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work

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Entanglement entropy vs entropy

I just read that if you have a pure density matrix state on a product space, then a way to define entropy in a subspace is to take the reduced density matrix state and define $S = 1- ...
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Why does this entropy change formula for heating water blow up at $T_{1}=0$?

My textbook says: Next we consider a more complicated problem: heating m grams of water, from $T_{1}$ to $T_{2}$. The entropy change is $$S_{2}-S_{1}=\int mc_{w} ...
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Is there a thermodynamic limit on how efficiently you can solve a Rubik's cube?

Suppose I build a machine which will be given Rubik's cubes that have been scrambled to one of the $\sim 2^{65}$ possible positions of the cube, chosen uniformly at random. Is it possible for the ...
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How does the entropy of an isolated system increase?

The change of entropy is defined $$\Delta S = \int \frac{dQ_\mathrm{rev}}{T}.$$ If a system is isolated the heat transfer between the system and the surroundings is zero ($dQ = 0$), thus $\Delta S = ...
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Is there a relation between (non-) existence of magnetic monopoles and thermodynamics?

This question follows on previous work on connections between (other) areas of physics and thermodynamics as in here, here and even here. P. Dirac (an electrical engineer initially) was one of the ...
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Why the amount of entropy increase to a system is less when heat is added to a higher temperature system than to a lower one?

As I understand it, statistically this means that a fall from a high temperature (say $300\text{ K}$) to a middle temperature ($200\text{ K}$), and an increase from say ($100\text{ K}$) to ($200\text{ ...
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Prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy

I'm trying to prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy. Now, for this to make sense I should give some definitions. System $A$ lives in Hilbert space ...
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Is the equilibrium state in thermodynamics a consequence of the second law of thermodynamics?

Is the thermal equilibrium state the state of maximum entropy? Is it a consequence of the second law of thermodynamics?
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Behavior of maximum entropy states in a closed system?

As I understand it, entropy is a measure of the number of permutations of microstates of a system possible, without changing the observed 'macrostate variables' / measurements or properties of a ...
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What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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How does the universe store information

I have read that entropy is responsible for the storage of information in the universe; that information increases with entropy increase. and that information is never lost. Is this correct? But ...
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Entropy change at varying volumes

I have two questions both related to each other: 1.What is the effect of change in volume (whether increasing or decreasing), of a system, under isothermal conditions? How does this change in ...
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Is the flatness of space a measure of entropy?

This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes. The main reason is that gravity is ...
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Definition of Entropy for reversible and irreversible process

$\int \dfrac{\delta Q}{T}$ can't be used to calculate entropy of an irreversible process. If you happen to know heat supplied and temperature at which it is supplied for just an instant. Can you then ...
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Is Boltzmann distribution contradicting with the fundamental assumption of statistical thermodynamics?

In equilibrium statistical physics the fundamental assumption of statistical thermodynamics states that the occupation of any microstate is equally probable (i.e. $p_i=1/\Omega, S=-k_B\sum p_i\,{\rm ...
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Can entropy of Universe be constant?

If I understand entropy correctly, then for example two objects orbiting a centre of mass have lower entropy than when said objects eventually crash into each other and form a new one. So let's say ...
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What was the entropy of the universe at the time of the Big Bang?

(I asked this question in Philosophy.SE; but I was advised to direct it here, despite it is, in my opinion, somewhat too speculative for physics.SE). High entropy generally means high disorder; and ...
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Will Ice Cubes Form Quicker when Made from Hot Water or Cold Water? [duplicate]

When you put water in the freezer you can make Ice Cubes. But does the time taken for these Ice Cubes to form decrease or increase when the water which is used is hotter or colder?
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The initial presumed temperature of the universe is derived from data?

When people mention the BBT (*) they assume that it is hot. As late as 1988 it was scientifically proposed a cold BB model (WP) The initial presumed temperature of the universe is derived from ...
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How does the formation of a solar system not break the second law of thermodynamics?

Please forgive: I am a layman when it comes to physics and cosmology, and have tried finding an answer to this that I can understand, with no luck. As I understand it, the solar system evolved from a ...
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Light Polarizer and the Second Law of Thermodynamics

I have stumped myself with a thought experiment of my own devising. Suppose I take a beam of wholly depolarised, but otherwise plane wave light. Its von Neumann entropy per photon is $\log(2)$ nats ...
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Does entropy have a physical meaning?

Entropy is incredibly useful as a mathematical tool. But what does it actually mean? I understand that the Boltzmann entropy is defined by: $$S=k\ln{\Omega}$$ With $\Omega$ being the multiplicity ...
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Do the number of possible microstates increase as temperature decreases?

Entropy change, $\Delta{S}$, can be found from the $\frac{1}{T} - Q$ graph. When the temperature doesn't change during the dispersal of heat energy in the system, the area under the graph is more, ...
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First law of thermodynamics [closed]

In the first law of thermodynamics, we learned that $W$ and $Q$ are path-dependent quantities, but how are $Q$ and $W$ defined? I mean $W = \int_{\gamma} p(s) ds$ would be one possibility, where ...
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Exorcism of Maxwell's Demon

I am possessed! Yes, with the thinking that if there is actually a Maxwell's Demon, then it would open the negligible weighted door which would ultimately make the second law invalid. But really can ...
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Can ice have a higher entropy than water?

I've leant that entropy is a state of randomness, and that solids have a more structured form, therefore having less entropy. However, I saw a YouTube comment stating the following: a liquid NOT ...
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Why Does Air Hold More Water When the Air is Warmer?

I know that when the temperature of the air rises, the maximum amount of Water it can hold before the water condenses to water droplets increases. But why is this - has it got something to do with ...
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Isentropic efficiency of gas expansion process

let a compressed gas expand. If the process is isentropic, the relationship between its temperature before expansion, and its temperature after expansion is related to its heat capacity ratio. The ...
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Probability polytope and entropy

Say I have a trit, for which all possible distributions are described by the positive surface of the diamond polytope (the surface being an equilateral triangle). The centre of this triangle is the ...
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Is there any proof for the 2nd law of thermodynamics?

Are there any analytical proofs for the 2nd law of thermodynamics? Or is it based entirely on empirical evidence?
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Residual Entropy - Third Law

I've been told that many systems possess some residual entropy at absolute zero. This would seem to disagree with the 3rd Law of Thermodynamics? How can this be explained physically speaking? I am ...
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No Hair systems and black hole entropy

To my understanding, a black hole is a no hair system. So it can be described just by its mass, spin and charge. In other words it does not differentiate where its mass comes from, so it could be made ...
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Entropy change in irreversible heat flow

For an irreversible heat flow from an object $A$ at temperature $T_A$ and another object $B$ at temperature $T_B < T_A$ , I'd like to know how to evaluate the change in entropy using the following ...
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How did Planck use the concept of statistical entropy in trying to understand the meaning of his own law?

I was reading Introducing Quantum Theory: A graphic guide (by J.P.McEvoy & Oscar Zarate) and came across Planck's predicament of understanding his very own law that accurately explained the ...
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If entropy is increasing does it mean universe is non-deterministic?

I watched some video where they said entropy can be considered as information. They also stated that universe's entropy is always increasing... Now here comes the problem my IT mind can't understand: ...
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Physical Meaning Of $ dQ/T $ Regarding Clausius Inequality: Is it related to Energy Loss in form of heat or Something Else?

What is the physical meaning of term $ dQ/T $ in Clausius Inequality $ dQ/T \le dS $ ? Physically we can relate entropy to number of microstates of a system, which relates to number of possible ...
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Change in Shannon entropy of a quantum circuit of Hadamard gate and a loop

The following Q&A about reversible computing is available here. It has listed a number of practical scenarios where a reversible circuit can still be dissipating heat. Let's assume that none of ...
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What are the hypothetic cases when entropy of a closed system may decrease? [closed]

What are the hypothetical possibilities that entropy of a closed system may decrease? I would accept plausible but hypothetical setups. For instance, Non-trivial timeline topology (closed timelike ...
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Was the Universe's entropy equal to zero at the Big Bang? Is zero-entropy state unique?

It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state. Does this claim specifically mean that the entropy of the initial universe was zero? ...
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Deriving an Expression for Helmoltz free energy

Given the equations of states for an isolated system: $$E=\frac32 pV$$ $$p=aVT^4$$ I was asked to find the Helmoltz free energy per particle, $F=E-TS$, as a function of $T$ and $V$. I began with the ...
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Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
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Was the Big Bang actually cold?

As I understand, from watching the Discovery Channel, the total amount of energy in the universe is zero. As such, people like Hawking explain that the universe can be created out of nothing ...
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Integrating factor $1/T$ in 2nd Law of Thermodynamics

How would you prove that $1/T$ is the most suitable integrating factor to transform $\delta Q$ to an exact differential in the second law of thermodynamics: $$dS = \frac{\delta Q}{T}$$ Where $dS$ is ...
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Is entropy related to Poincare recurrence time?

One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after ...
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second law of thermodynamics

I'm a high school rookie learning thermodynamics right now by myself. I got really confused that the second law of thermodynamics states that the entropy of the universe is always increasing. If the ...
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How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
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Why do you want to maximise the entropy when deriving Boltzmann's distribution?

I am sure this has a simple answer, but I can't seem to get my head around in at the moment. I am going through the derivation of the Boltzmann distribution through maximising entropy through the ...
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The relationship between the two statistical mechanical definitions of entropy

It seems like similar questions have been asked here; hopefully my question is not a duplicate. I am reading my textbook on the statistical mechanical definitions of entropy, and I am very confused ...
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Death by entropy

An idea struck me as I was walking to class today. According to Wikipedia, entropy is defined as the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a ...
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Why does the law of increasing entropy, a law arising from statistics of many particles, underpin modern physics?

As far as I interpret it, the law of ever increasing entropy states that "a system will always move towards the most disordered state, never in the other direction". Now, I understand why it would ...