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

5
votes
4answers
510 views

Chance of objects going against greater entropy?

My book uses the argument that the multiplicities of a few macrostates in a macroscopic object take up an extraordinarily large share of all possible microstates, such that even over the entire ...
27
votes
6answers
3k views

Why is information indestructable?

I really can't understand what Leonard Susskind means when he says that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He ...
13
votes
5answers
1k views

Is a world with constant/decreasing entropy theoretically impossible?

I'm not 110% sure exactly what I mean by this question. It was sparked by a friend who said he wished the law of entropy were reversed, so he wouldn't have to worry about cleaning the bathroom. ...
9
votes
6answers
717 views

How do you prove the second law of thermodynamics from statistical mechanics?

How do you prove the second law of thermodynamics from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide.
8
votes
6answers
1k views

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
8
votes
5answers
4k views

Why was the universe in a extraordinarily low-entropy state right after the big bang?

Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and ...
15
votes
6answers
1k views

How can it be that the beginning universe had a high temperature and a low entropy at the same time?

The Big Bang theory assumes that our universe started from a very/infinitely dense and extremely/infinitely hot state. But on the other side, it is often claimed that our universe must have been ...
2
votes
3answers
145 views

How does the evolution 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 ...
17
votes
4answers
2k views

How do you prove $S=-\sum p\ln p$?

How does one prove the formula for entropy $S=-\sum p\ln p$? Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law ...
6
votes
3answers
1k views

Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in e=mc^2. Maxwell's Demon can turn information supplied ...
9
votes
3answers
2k views

Why does the low entropy at the big bang require an explanation? (cosmological arrow of time)

I have read Sean Carrol's book. I have listened to Roger Penrose talk on "Before the Big Bang". Both are offering to explain the mystery of low entropy, highly ordered state, at the Big Bang. Since ...
37
votes
5answers
2k views

What is information?

We're all familiar with basic tenants such as "information cannot be transmitted faster than light" and ideas such as information conservation in scenarios like Hawking radiation (and in general, ...
8
votes
3answers
1k views

How efficient is a desktop computer?

As I understand it (and admittedly it's a weak grasp), a computer processes information irreversibly (AND gates, for example), and therefore has some minimum entropy increase associated with its ...
5
votes
3answers
8k views

Do magnets lose their magnetism?

I recently bought some buckyballs, considered to be the world's best selling desk toy. Essentially, they are little, spherical magnets that can form interesting shapes when a bunch of them are used ...
1
vote
2answers
215 views

Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question. The ...
3
votes
1answer
240 views

Should entropy have units and temperature in terms of energy? [duplicate]

I've been thinking about entropy for a while and why it is a confusing concept and many references are filled with varying descriptions of something that is a statistical probability (arrows of time, ...
21
votes
7answers
953 views

How is $\frac{dQ}{T}$ measure of randomness of system?

I am studying entropy and its hard for me to catch up what exactly is entropy. Many articles and books write that entropy is the measure of randomness or disorder of the system. They say when a gas ...
17
votes
5answers
2k views

Where does deleted information go?

I've heard that, in classical and quantum mechanics, the law of conservation of information holds. I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
14
votes
3answers
3k 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?
12
votes
5answers
2k views

Can a single classical particle have any entropy?

recently I have had some exchanges with @Marek regarding entropy of a single classical particle. I always believed that to define entropy one must have some distribution. In Quantum theory, a single ...
6
votes
1answer
1k views

Clear up confusion about the meaning of entropy

So I though, and was told, that entropy is the amount of disorder in a system. Specifically the example of heat flow and it flows to maximize entropy. To me this seemed odd. This seemed more ordered ...
6
votes
1answer
356 views

Motivation for maximum Renyi/Tsallis entropy

The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy. Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy ...
4
votes
4answers
478 views

Entropy as an arrow of time

From what I understand, entropy is a concept defined by the experimentalist due to his ignorance of the exact microstate of a system. To say the number of accessible microstates $W$ of the universe is ...
11
votes
2answers
394 views

black hole no-hair theorems vs. entropy and surface area

I was revisiting some old popular science books a while ago and two statements struck me as incompatible. No-hair theorems: a black hole is fully-described by just a few numbers (mass, spin etc) ...
7
votes
1answer
389 views

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 ...
2
votes
1answer
202 views

Connection between Kolmogorov entropy and Boltzmann entropy

http://math.stackexchange.com/questions/527384/what-is-the-connectivity-between-boltzmanns-entropy-expression-and-shannons-en mentions a relationship between Shannon entropy and Boltzmann entropy. Is ...
5
votes
1answer
256 views

What is the entropy of the universe today?

What's the entropy of the universe today? How does one go about calculating this? I've heard the statement that black holes account for the bulk of the entropy in the universe today, but don't know ...
3
votes
3answers
217 views

Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
2
votes
1answer
259 views

Black hole entropy

Bekenstein and Hawking derived the expression for black hole entropy as, $$ S_{BH}={c^3 A\over 4 G \hbar}. $$ We know from the hindsight that entropy has statistical interpretation. It is a measure ...
1
vote
0answers
163 views

What is Mathematical formulation of entropic Gravitational force?

There are people proposing the possibility of using entropic force to explain the gravity force between objects. The emphasis is that entropy is more fundamental than energy. It is the closest study ...
1
vote
3answers
381 views

Mathematical proof of non-negative change of entropy $\Delta S\geq0$

I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a ...
0
votes
2answers
178 views

Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link ...
5
votes
7answers
1k views

Entropy and Crystal Growth

I was reading about growing single crystals and I'm a little confused about this - In most crystal growing processes, a "seed crystal" is used, and the rest of the material crystallizes on the seed ...
4
votes
3answers
189 views

Problem about entropy

Combining the first and second law of thermodynamics we can get the following equation $$TdS=dU-P_{ext}dV$$ First question: Is this equation applicable for irreversible processes such that that ...
4
votes
1answer
161 views

Is this derivation of Black Hole entropy viable?

This question is motivated by this one. Suppose $l$ is the minimum measurable unit of length. What is entropy of a spinless particle contained in this interval? We know that entropy of a two-level ...
3
votes
0answers
153 views

Does natural unit of information and entropy, nat, play special role in the freebit picture?

Please refer this question to understand why I consider the freebit picture important. In short, it is conjectured, that for certain real systems the most complete physical description possible ...
3
votes
3answers
465 views

How bright can we make a sun jar?

A sun jar is an object that stores solar energy in a battery and then releases it during dark hours through a led. Assume: a $65cm^2$ solar panel a 12h/12h light/dark cycle insolation of ...
1
vote
2answers
929 views

What is the physical or mathematical meaning of the Gibbs-Duhem equation?

The Gibbs-Duhem equation states $$0~=~SdT-VdP+\sum(N_i d\mu_i),$$ where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?
15
votes
4answers
3k views

Why does the nature always prefer low energy and maximum entropy?

Why does the nature always prefer low energy and maximum entropy? I've just learned electrostatics and I still have no idea why like charges repel each other. ...
18
votes
3answers
526 views

Intuitive understanding of the entropy equation

In thermodynamics, entropy is defined as $ d S = \dfrac{\delta q_{\rm }}{T}$. This definition guarantees that heat will transfer from hot to cold, which is the second law of thermodynamics. But, why ...
15
votes
5answers
2k views

Why isn't absolute $0 K$ temperature possible?

So $T$ is defined as $$T = \left(\frac{\partial E}{\partial S}\right)$$ and $S$ is defined as $$S = k_B \ln \Omega$$ where $\Omega$ is the number of accessible states of the system for a given ...
12
votes
4answers
868 views

Ignorance in statistical mechanics

Consider this penny on my desc. It is a particular piece of metal, well described by statistical mechanics, which assigns to it a state, namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
7
votes
5answers
1k views

Perpetual motion machine of the second kind possible in nano technology?

First of all sorry for my English - it is not my native language. During my engineering studies at the university the thermodynamics professor told us that the "second law of thermodynamics is not ...
13
votes
5answers
2k views

Entropy of radiation emitted into space

In several papers I see something equivalent to the following expression for the entropy of radiation given by an astronomical object such as the Sun (assuming the object can be approximated as a ...
8
votes
2answers
240 views

Casimir effect as an entropic force

When I first learned about the depletion interaction, my initial reaction was that it looks very similar to the Casimir effect. On making this remark to the professor, he replied somewhat mystically: ...
7
votes
5answers
1k views

How is thermodynamic entropy defined? What is its relationship to information entropy?

I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states. How is ...
5
votes
0answers
98 views

Victorian cosmology after the second law of thermodynamics but before relativity?

In the 19th century, most astronomers adopted an island universe model, in which our galaxy was the only object in an infinite space. They didn't know that the "spiral nebulae" were other galaxies. ...
4
votes
2answers
343 views

The statistical nature of the 2nd Law of Thermodynamics

Ok, so entropy increases... This is supposed to be an absolute statement about entropy. But then someone imagines a box with a 10 particle gas, and finds that every now and then all particles are in ...
4
votes
3answers
278 views

Entropy and Information

Several posts and my classes in thermodynamics equate increase in entropy with loss of information. Shannon clearly showed that the information content of a message is zero when its entropy is zero ...
7
votes
2answers
1k views

How is information related to energy in physics?

I recently attended a talk by Dr. Ravi Gomatam on 'quantum reality', where the speaker suggested, that conservation of energy is not a fundamental law, and is conditional, but the conservation of ...