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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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 ...
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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 ...
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987 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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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465 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.
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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 ...
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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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333 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 ...
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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) ...
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955 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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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331 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 ...
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Statistical Entropy and Information theory

I am having trouble in understanding the following concepts : Pg 231 Appendix B of the link ...
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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 ...
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441 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 ...
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789 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?
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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. ...
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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 ...
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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 ...
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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 $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
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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 ...
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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 ...
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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 ...
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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: ...
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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 ...
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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 ...
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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 ...
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Significance for LQG of Sen's result on entropy of black holes?

Sen 2013 says, ...we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions [...] For Schwarzschild black holes in ...
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What physical processes may underly the collisional term in the Boltzmann equation, and how do they increase entropy?

Consider particles interacting only by long-range (inverse square law) forces, either attractive or repulsive. I am comfortable with the idea that their behavior may be described by the collsionless ...
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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. ...
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Is there a mechanism for time symmetry breaking?

Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
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The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
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What are the arguments towards the Life-and-Entropy relation?

I've heard it from a few people, and I've seen it popup here in the site a couple of times. There seems to be speculation (and studies?) towards this idea, and this is what I've picked up so far: ...
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When is entanglement entropy the same as free energy?

I am given the feeling that there exists scenarios when this equality holds. Can anyone state/refer to the situations? One case that I hear of is that for $2+1$ CFTs the entanglement entropy ...
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Does entropy really always increase (or stay the same)? [duplicate]

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, ...
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Relation between Casimir and hydrophobic effects

Background Some years ago I was studying "Fundamentos de biología" (Biology fundamentals) and learned how the lipids create a bilayer due to the water repulsion. Some time later I learned that this ...
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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 ...
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Connection between entropy and energy

An isolated system $A$ has entropy $S_a>0$. Next, the isolation of $A$ is temporarily violated, and it has entropy reduced $$S_b ~=~ S_a - S,\space\space\space S\leq S_a.$$ Is it true to say: the ...
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Energy of unmixing

Mixing of two different fluids is associated with an increase of entropy. Conversely, separation of two gases must be associated with a decrease of the entropy of the two fluids. Is there a minimum ...