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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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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3answers
183 views

Entropy and the uncertainty principle

According to the second law of thermodynamics, the total entropy of the Universe must always increase after any interaction (as I understand). So in the hydrogen atom, the electron has a high ...
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2answers
100 views

“Violation” of the Second Law

I can't reconcile some facts about entropy and irreversibility. This depresses me, because I feel I can't quite grasp the importance of entropy. I will illustrate my problems with an example given by ...
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1answer
30 views

Can you choose the variables of a state function?

I'm confused. I was first introduced to entropy as a state function of internal energy and volume $$S(U,V) \Rightarrow dS = C_v\frac{\mathrm{d}T}{T} - p\frac{\mathrm{d}V}{T} $$ wich is the ...
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1answer
52 views

Entropy / Structure Relations

I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? The further a system is from its maximum ...
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1answer
97 views

Explicit form of the entropy production in hydrodynamics

I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the ...
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1answer
53 views

Helmholtz free energy from a relation for entropy

The Legendre transformation defines the helmholtz free energy (at least according to my lectures) as: $F(T,V,N)=E-TS$ It also says to start with $E(S,V,N)$ and $T=\frac{\partial{E}}{\partial{S}}$ ...
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0answers
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Has any possible non-extensive entropy been classified?

How many non-extensive entropies do exist? Tsallis, Havrda-Chavrat, Renyi, Kaniadakis, Sharma-Mittal,... To be more precise, I am wondering if some classification like those of "finite" or Lie groups ...
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1answer
62 views

How to calculate the Wald functional?

I want to calculate the Wald functional for arbitrary higher curvature Lagrangians - like getting equation 6.31 from 6.30 in this paper. A priori the above looks like an extremely complicated ...
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5answers
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What is information?

We're all familiar with basic tenets 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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2answers
33 views

Entropy change at varying temperatures?

Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a specific temperature. Reversivility means that the temperature of the system must remain constant ...
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4answers
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Difference between heat capacity and entropy?

Heat capacity $C$ of an object is the proportionality constant between the heat $Q$ that the object absorbs or loses & the resulting temperature change $\delta T$ of the object. Entropy change is ...
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1answer
67 views

Definition of entropy in nonequilibrium states

Thermodynamical definition of entropy $$S(p)=-\int p\ln p~dx$$ is defined only on equilibrium system. But why can't we use it for non-equilibrium system? Is there a well-accepted definition for it?
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1answer
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How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
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1answer
49 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{ ...
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1answer
40 views

Regarding the 'Arrow of Time'

I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their ...
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2answers
53 views

Thermodynamics of scattering theory

I have a couple of conceptual questions regarding the thermodynamics of scattering. Any partial answer or argument will be appreciated. For the sake of discussion, consider the scattering of ...
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3answers
82 views

Is there a minimum energy content of information, other than 0 Joules?

Lets say I want to send the bit string 010110 to someone. Is there a theoretical lower bound on the energy needed to do this?
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2answers
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Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
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3answers
249 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 ...
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2answers
147 views

Is the second law of Thermodynamics an immense tautology?

Let's imagine for a second a system that is changing constantly from one microstate to another one. It could be a given volume of a gas with its atoms moving and bouncing around, or a deck of cards ...
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1answer
45 views

Does the entropy of a system vary in the equilibrium?

I am not physicist and this question may seem trivial. But I understand that in the equilibrium the magnitudes such as temperature or volumen do not vary. Is the same for entropy? My logical says that ...
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2answers
224 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
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0answers
34 views

Entropy of an oscillator in Einstein's solid

This is a homework problem and I need help with it. A solid's (Einstein's model) oscillators are in the first excited state on average. How much entropy does one oscillator have? What I've tried so ...
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1answer
106 views

Gravity and the Second Law of Thermodynamics [duplicate]

I was wondering about the hypothetical - and apparently improbable - heat death of the Universe when I stumbled upon this seeming contradiction. A certain volume of space with a uniform distribution ...
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2answers
119 views

Who invented the perfume bottle thought experiment?

A common thought experiment used to explain the second law of thermodynamics, the "arrow of time", etc. is perfume escaping from an opened perfume bottle; the perfume is likely to diffuse into the ...
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Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
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1answer
94 views

Thermodynamics for Dummies: Entropy and temperature

I do not study physics and I have never had a course in thermodynamics. I have no idea what it is about, but I am currently taking a course where we had something about entropy. Would be great if ...
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6answers
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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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3answers
82 views

Is Fourier's law of conduction a consequence of the second principle?

In classical thermodynamics courses, entropy is often motivated by the need to justify that heat flows from high temperatures zones to lower temperatures zones: this is seen as a consequence of ...
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5answers
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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 ...
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1answer
236 views

How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...
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3answers
104 views

Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
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2answers
82 views

Does all information in the universe come from the observer?

In absence of the observer any system undergoes unitary evolution, that is reversible evolution without entropy change. It is believed that the initial state of the universe had very low entropy, ...
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61 views

Dimensionless entropy interpretation

Measuring temperature in joules instead in the artificial units of Kelvin would render entropy as a dimensionless quantity. This is quite appealing since entropy has always been quite a misterious ...
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3answers
154 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 ...
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2answers
63 views

What is entropy of the universe? [duplicate]

What is entropy of the universe? What is the change in entropy of our universe? Is this change increases or decreases? If the entropy of universe keeps on increasing then what are the consequences? Is ...
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4answers
95 views

Entropy and dark matter structure

Inspired by this question. I believe that the usual explanation that preserves the second law of thermodynamics as an astrophysical gas cloud collapses under gravity is that the gas must heat and ...
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3answers
100 views

Are galaxies, stars, planets, and ultimately life in violation of the second law of thermodynamics? [duplicate]

How can we think about entropy in these situations? To my knowledge all of these structures are born out of gravitational interaction. However, it would seem that the formation of these more organized ...
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0answers
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BTZ Black Hole Central Charge and Conformal Weight

I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
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3answers
82 views

Potential energy & entropy of three particles

Let me first say that I am not a physicist, but I am trying to make a simulation on my computer and I have the following question. Let's consider that we have three free charges that somehow can ...
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2answers
101 views

How can heat turn into light

I am confused about how hot surfaces can radiate light to their surroundings. When I shine a light on a surface the light turns to heat spontaneously, and when I leave that hot surface it radiates ...
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1answer
91 views

How to measure Entropy?

While $$\delta Q=T\ dS$$ allows for obtaining the entropy change of an isolated system in equilibrium by measuring the heat exchange with the environment, I was wondering whether there are ways to ...
6
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1answer
47 views

Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
2
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0answers
50 views

Is the second law of thermodynamics a real law? [duplicate]

Everytime I ask people why the second law of thermodynamics is true, they say because the probability of entropy increasing is very large. This for some reason doesn't seem right for me. Just because ...
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4answers
362 views

Mathematical proof of the Second Law of Thermodynamics [duplicate]

Is there some book or paper that formalizes statistical mechanics, like some people have done with relativity, and proves the second law of thermodynamics from more foundational axioms?
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1answer
51 views

What is the difference between a low vs. high entropy plasma just after and before a singularity occurs?

Although it appears that the universe is not closed (since it is accelerating) I have been reading different websites on how the universe would look like if it was closed and the big crunch did occur. ...
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1answer
53 views

What is intrinsic gravitational entropy?

What is intrinsic gravitational entropy? Does it have to do with dark matter or coarse graining in the universe? Is it unique to general relativity, or there are predictions from quantum mechanics as ...
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3answers
69 views

Does the entropy of an adiabatically isolated system stays the same after we decrease/increase the pressure?

Even if the system is isolated and there is no heat exchange with surroundings, shouldn't the decrease/increase of pressure result in increase/decrease of entropy? Does this property of an ...
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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.