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

learn more… | top users | synonyms

2
votes
1answer
168 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 ...
4
votes
1answer
70 views

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 ...
3
votes
4answers
315 views

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 ...
10
votes
6answers
864 views

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 ...
-3
votes
1answer
76 views

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 ...
1
vote
0answers
77 views

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 ...
1
vote
0answers
48 views

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: ...
0
votes
2answers
907 views

Entropy and chemical potential of an ideal gas

I am reading Schroeder's book "Thermal Physics". One calculation in the text was not quite clear to me. The entropy of an ideal gas is given by the Sackur-Tetrode equation: $$ ...
8
votes
4answers
649 views

Existence of negative temperatures and the definition of entropy

How negative temperatures can be possible has been treated on StackExchange before (several times in fact), but in light of some recent academic discussion, most of these answers seem to be possibly ...
4
votes
1answer
232 views

No hair theorem and black hole entropy

The no hair theorem says that black holes rapidly converge to a state that is completely described just by their mass, spin and charge. Black hole thermodynamics says that the black hole entropy is ...
1
vote
1answer
39 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 ...
13
votes
2answers
204 views

Doesn't entropy increase backwards in time, too?

In statistical explanations of entropy, we can often read about a (thought) experiment of the following sort. We have a bunch of particles in box, packed densely in one of the corners. We assume some ...
1
vote
1answer
183 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 ...
0
votes
0answers
64 views

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- ...
1
vote
2answers
116 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} ...
35
votes
6answers
5k views

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 ...
3
votes
4answers
1k views

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 = ...
2
votes
2answers
170 views

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 ...
0
votes
3answers
85 views

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{ ...
2
votes
1answer
67 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 ...
0
votes
1answer
36 views

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?
0
votes
0answers
30 views

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 ...
8
votes
10answers
4k views

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 ...
0
votes
0answers
66 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 ...
0
votes
1answer
50 views

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 ...
14
votes
3answers
371 views

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 ...
2
votes
0answers
122 views

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 ...
1
vote
1answer
124 views

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 ...
2
votes
2answers
97 views

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 ...
10
votes
5answers
1k views

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 ...
15
votes
5answers
1k views

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 ...
1
vote
0answers
22 views

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?
0
votes
0answers
23 views

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 ...
6
votes
4answers
332 views

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 ...
5
votes
4answers
184 views

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 ...
6
votes
3answers
599 views

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 ...
2
votes
2answers
164 views

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, ...
2
votes
2answers
99 views

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 ...
6
votes
4answers
2k views

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 ...
5
votes
2answers
6k views

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 ...
1
vote
2answers
116 views

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 ...
0
votes
0answers
142 views

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 ...
0
votes
0answers
20 views

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 ...
15
votes
3answers
5k views

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?
0
votes
2answers
124 views

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 ...
0
votes
0answers
42 views

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 ...
0
votes
2answers
83 views

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 ...
2
votes
1answer
50 views

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 ...
6
votes
2answers
180 views

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: ...
1
vote
1answer
79 views

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 ...