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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Will the black hole size increase?

I was thinking about the following thought experiment, but wasn't sure about its outcome. Suppose there is a black-hole and I enter it with a partitioned box containing two different gases on either ...
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Proving that Measurement increases von Neumann entropy

Let $V$ be a finite dimensional complex inner product space. Let $\mathcal{M}$ be the classical sample space of measurement outcomes that may occur in a given experiment, and $M_\mu$, $\mu \in ...
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At an instant, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges?

Question: In principle, does a system of gravitational charges exhibit equivalent behavior to a time-reversed system of like electric charges? (At a single instance in time?) Additional Notes: I am ...
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Thermodynamics of binary symmetric channels

I am reading this very interesting paper: http://m.iopscience.iop.org/1751-8121/41/40/402002/pdf/1751-8121_41_40_402002.pdf about thermodynamics of channels in information theory. More generally, ...
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About parametrizing quadratic fluctuations in the metric about $AdS_2 \times S^2$

I am referring to the contents of page 20-23 of the paper, http://arxiv.org/abs/1108.3842.pdf Equation 4.5 seems to suggest that one wants to restrict the metric fluctuations $h$ to a subset such ...
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How would we perceive time going backwards? [closed]

I haven't taken Physics in University. Lately, I've been reading about some of the branches of physics through Wikipedia. I read several times that many of the theoretical models do not explain why ...
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Classical and Semi-classical treatments of the ideal gas

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where $Z(1)$ is the single particle partition function and $N$ is the ...
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1answer
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Entropy is constant. How to express this equation in terms of pressure and density?

In hydrodynamics of an ideal, non-compressive flow we use 5 variables: pressure $p$, density $\rho$ and velocity field $\mathbf{v}$. So we need 5 equations. Landau's "Hydrodynamics" states that the ...
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1answer
131 views

Mathematical form of chemical potential difference and entropy production

I'm trying to understand the form of the 'force' which drives chemical reactions, ie. the difference in chemical potential, also sometimes called the 'affinity'. $$\Delta \mu = - kT ln ...
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208 views

Entropy $dQ=TdS$ and Work $dW = -pdV$ conditions?

What are the conditions in order for the equations: Entropy $dQ = TdS$ and Work $dW = -p dV$ to work? I think for $dQ = T dS$, it must be a reversible process? But for $dW = -p dV$, shouldn't it ...
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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 ...
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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 ...
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108 views

Information or Matter or Energy

Which one is the most fundamental of the universe? What it is made of? Physicists are searching for unique and fundamental form. The question is , information is more fundamental than energy ? ...
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1answer
82 views

consequences of universe in which second law of thermodynamics does not hold [closed]

What would happen if the second law of thermodynamics was not there for governing in every day processes. Can a universe exist and evolve if the second law of thermodynamics does not exist in first ...
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62 views

Does causality alone resolve the mathematical ambiguity of expressing physical systems?

Newton's 2nd law of motion is most often written in the differential form $\sum F = {dp \over dt} $ but can also be expressed in an integral form $ p = \int\sum F dt $ Each form of expressing ...
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57 views

Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a biparte system $AB$, described ...
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2answers
73 views

Entropy before and after collapse of the wavefunction/ and interpretation?

Seems like it might be pretty rudimentary but I want to see if my thinking is on the right track as well as what the result means. The question is, is the entropy of the collapse of a wavefunction or ...
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204 views

Why aren't we surrounded by Black holes?

The Bekenstein bound is a limit to the amount of entropy a thermodynamical system can have. The bound is given by the following expression: \begin{equation} S \leq \frac{2 \pi k R E}{\hbar c} ...
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85 views

The entropy of the universe in an irreversible cycle [closed]

Suppose we have an ideal gas performing an irreversible cycle composed by: an isothermal transformation at $T_{1}$; an isobaric transformation at $P_{A}$; an isothermal transformation at $T_{2}$; an ...
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entropy in Information theory vs thermodynamic?

We Now From Information Theory That Entropy Of Functions Of A Random Variable $X$ Is Less Than Or Equal To The Entropy Of $X$. Does It Break The Second Law Of Thermodynamic?
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1answer
226 views

Principle of Caratheodory and The Second Law of Thermodynamics

Background Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be ...
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124 views

Quantum entropy in term of density matrix

Why in von Neumann expression of quantum entropy we have trace of density matrix expression? Why don't off diagonal term play a role?
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223 views

Natural units of information

In physics entropy is usually measured in nats. I wonder is there a possible model of a physical system which has entropy of discrete number of nats? How particles and degrees of freedom should be ...
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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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1answer
110 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: $$ ...
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3answers
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Was the Universe's entropy equal to zero at the Big Bang? Is zero-entropy state unique?

It is postulated by many cosmologists that at the Big Bang time the universe was in an unusual low entropy state. Does this claim specifically mean that the entropy of the initial universe was zero? ...
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Homemade salad dressing separates into layers after it sits for a while. Why doesn't this violate the 2nd law of thermodynamics?

The oil, vinegar and other liquids in homemade salad dressing separate into layers after sitting for a while, making the mixture become more organized as time evolves. Why doesn't this violate the ...
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Entropy and how it applies to everyday activities like eating food

So I was eating a plate of food one day and thought of entropy. As I understand the definition of entropy, it is the logarithm of the number of arrangements or states the object in question can be in, ...
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Intuitively, why does removing solutes cost $k_B T$ of free energy per molecule?

I can calculate that if you want to, for example, desalinate water, you will have to pay a free energy cost of $k_B T$ for each ion you remove. In other words, removing an ion from a volume of water ...
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53 views

Is entropy a dynamical quantity [closed]

I am confused whether Entropy is a dynamical quantity or not. Gibbs entropy, and quantum mechanical Von Neumann entropy.
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532 views

Motivation for the use of Tsallis entropy

Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't ...
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43 views

On the relationship between entropy and chaotic noise

I have few conceptual questions related to application of chaos in communications. Kolmogorov-Sinai Entropy1 , Kolmogorov-Sinai Entropy2 and Kolmogorov-Sinai Entropy3 KS is an entropy metric for ...
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1answer
111 views

Definition of Information in Information Theory

I am not sure in which SE site I have to put this question. But since I have learnt Shannon Entropy in the context of Statistical Physics, I am putting this question here. In the case of Shannon ...
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65 views

Would it be possible to measure the change of entropy of a system? why?

To be more specific, what I mean is to measure it in a experiment. And if the answer is no, I want to know if it is principally impossible, or just impossible due to the technic limitation of our ...
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45 views

Lagrangian Field Entropy?

Has anyone investigated the inclusion of a field's entropy in its Lagrangian? I read from information theory that the entropy $H$ of a scalar field $\phi$ distrusted across space is defined as ...
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486 views

Is entropy of all systems zero at absolute zero?

Is the entropy of every system zero at the absolute zero? Or is it taken to be zero at the absolute zero? Are there systems that doesn't reach zero entropy even till absolute zero?
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1answer
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What precisely does the 2nd law of thermo state, considering that entropy depends on how we define macrostate?

Boltzmann's definition of entropy is $\sigma = \log \Omega$, where $\Omega$ is the number of microstates consistent with a given macrostate. If I understand correctly, this means that it only makes ...
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1answer
86 views

Entropy and Stability [closed]

What happens when you increase entropy in a system? Does it increase the instability? Is disorder the same as entropy?
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1answer
53 views

Thermodynamic entropy vs. quantum mechanical entropy

Is there a fundamental difference in the definition of entropy when considering the classical thermodynamic picture vs. the quantum mechanical picture, or are they both fundamentally equivalent?
5
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1answer
275 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 ...
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Bekenstein entropy black hole v.s Hawking entropy black hole

Historically, Bekenstein estimated the entropy associated with a black hole in 1973, obtaining: $$ S_B = \frac{\ln(2)k_Bc^3}{8\pi\hbar G}A. $$ He already acknowledges in his article that his estimates ...
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1answer
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Free Energy, Avialable Work in a reversible process

I was reading the Wikipedia page on Helmoltz Free Energy, http://en.wikipedia.org/wiki/Helmholtz_free_energy, and run across a point I cannot unravel. The discussion goes as follows, I reproduce it ...
4
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Why is adiabatic process isentropic?

I have read that adiabatic process is isentropic because there is no heat exchange in an adiabatic process and thus no change in entropy. But my question is - Even in adiabatic process, work can be ...
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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 ...
2
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Could CP violation be exploited to violate the second law?

I don't understand well CP-violation, but since it introduces a microscopic irreversible process, couldn't it be somehow exploited to decrease entropy? For instance, if we could somehow use it to bias ...
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1answer
54 views

Entropy in biological systems

I understand why entropy tends to a maximum; it is the tendency of a system to spend most of its time in the macroscopic state that corresponds to the largest number of phase cell configurations. How ...
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407 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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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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Immediately after the Big Bang, was the universe in a state of extremely low or extremely high entropy?

Phase space theory suggests that the largest course-graining region, $p$, in a phase space, $P$, is the point in the phase space with the highest entropy. As such, it is in thermal equilibrium with ...
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What is the effect of phase transition on the thermodynamic state variables of a material?

When a material undergoes a phase transition, it releases an amount of heat (under a specific temperature). So the effect of the phase transition on entropy would be equal to: \begin{align} ...