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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Laplace's demon and spontaneous symmetry breaking

One interpretation of Quantum mechanics is the hidden variable theory. This suggests that if we were to have a complete knowledge of the system at one time then the future states of the system are ...
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69 views

Entropy - does Heat Death occur in a closed system

Does heat death occur in a closed system? (Assuming you can theoretically have some sort of "closed system".
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Where does information go if thermodynamic death?

Often read that until Hawking the black holes were introducing a problem with information. Allegedly information should be unable disappear, while this was happening in classic black holes. What ...
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Is it possible to disprove water memory with an entropy argument?

Water memory was a controversial experiment claiming to provide an explanation supporting homeopathy. The results were largely dismissed as being tainted by experimental error. One possible mechanism ...
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Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
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60 views

Entropy and the $2^{nd}$ law of thermodynamics

I have just been introduced to the word "entropy" and as it is my understanding that it is a measure of the randomness and chaos of particles in as system. My textbook list the 2nd law of ...
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Callen Thermodynamics 2.8-2 help? [closed]

A two component gaseous system has a fundamental equation of the form $S=AU^{1/3} V^{1/3} N^{1/3} + \frac{BN_1N_2}{N}$ where $N=N_1+N_2$ and $A$ and $B$ are positive constants. A closed cylinder of ...
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Is information a form of energy? [closed]

To better describe my question, do the following experiment: Calculate x=12+26+67+71 Now you might have spent some time in getting the answer. You burnt sugar, you used up energy to get the ...
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110 views

How does this new theory of a possible infinitely old universe not violate the second law of thermodynamics

I read the following article: http://phys.org/news/2015-02-big-quantum-equation-universe.html And followed it back to this journal reference : http://arxiv.org/abs/1404.3093 It appears to be ...
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Entropy Inequalities

Hey I am reading this paper Entropy Inequalities by Araki and Lieb. I am trying to prove the following lemma: $$S^1+S^2\leq S^{12}+S^{23}$$ using the following lemmas: ...
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What is the interpretatation of individual contributions to the Shannon entropy?

If $X=\{ x_1,x_2,\dots,x_n\}$ are assigned probabilities $p(x_i)$, then the entropy is defined as $\sum_{i=1}^n\ p(x_i)\,\cdot\left(-\log p(x_i)\right).$ One may call $I(x_i)=-\log p(x_i)$ the ...
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Ternary dimensioned density matrix

I am currently reading this paper: Entropy Inequalities by Araki and Lieb (project Euclid link). And I am not able to understand one step: $${\rm Tr}^{123}\left(\rho^{12}\rho^{23}\right)={\rm ...
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22 views

What can I do with specific entropy and quality on a state (Rankine Cycle)

I've been working some Thermodynamics problems on Power Cycles and I have noticed that if I'm given a specific quality at the exit of the turbine and considering the adiabatic process I will have two ...
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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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73 views

How does the entropy change during the cooling of a hot coffee in a cold cup?

The second Law of Thermodynamics states that entropy always increases in the universe: things become more disorganised. This means, that if I have a hot coffee in a cold cup, then the heat will ...
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Space-Time and Entropic gravity [closed]

Gravity warps space-time, and Gravity can be thought of as Entropy. (Entropic gravity) So, as spacetime expands, how is space-time Entropy (or the inverse of gravity) effected? (If this is a noob ...
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54 views

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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59 views

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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42 views

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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Ideal chain / entropic spring - what is the *microscopic* force?

The ideal chain is the classic example of an entropic force. Usually one derives this force from the fundamental relation describing forces in the canonical ensemble: $$ \tag 1 F = (\partial \langle E ...
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Does Noether's theorem apply to entropy?

Entropy appears to have a translation symmetry - adding some constant value to it doesn't appear to my fairly rudimentary understanding of physics alter the actual physics. Is this correct? Now ...
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Is entropy absolute (as in absolute temperature)?

Following this question on the Entropy at the Big Bang where I asked: Since Entropy always increases (in general); its expected that the entropy at the beginning of the universe should be the ...
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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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Entropy of loops in the PV plane

The change in entropy of the Carnot and reversible cycles is said to be 0. Several other loops are supposed to have a non-negative change in entropy. This presents 2 problems which I cannot ...
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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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Entropy of the whole universe

In "Thermal Physics", Charles Kittel proves that entropy always increases in systems when the degree of freedom are increased (adding particles, adding energy, expanding volume, etc ). I started to ...
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94 views

The Big Crunch and perceived entropy

I'm aware of the Big Crunch theory, that once at capacity, the universe may collapse in on itself. Hawking once theorized that time may go backwards during this crunch. So, that got me thinking: how ...
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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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Why does heat added to a system at a lower temperature cause higher entropy increase?

Entropy is defined in my book as $\Delta\ S = \frac{Q}{T}$. To derive the formula it says that entropy should be directly proportional to the heat energy as with more energy the particles would be ...
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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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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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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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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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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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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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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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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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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 an irreversible process

I have just started learning thermodynamics and the concept of entropy confuses me. Suppose I have a gas in a cylindrical container fitted with a piston. I take it through an adiabatic irreversible ...
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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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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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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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How does the second law of thermodynamics follow from low entropy of early universe?

One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical ...
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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 ...