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

0
votes
2answers
22 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
28 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 ...
5
votes
2answers
62 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: ...
2
votes
1answer
47 views

How does the second law of thermodynamics follow from low entropy of early universe?

One of the explanations of the second law of thermodynamics is that it goes back to the low entropy in the early universe (How do you prove the second law of thermodynamics from statistical ...
1
vote
1answer
30 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 ...
2
votes
1answer
474 views

Difficulties with understanding total entropy change and unavailabillty

Of course, I know the fact that the entropy of an isolated system never decreases. Neverthless what makes me confused about the entropy(or change of entropy) of an isolated system is the explanation ...
0
votes
1answer
40 views

Change in Shannon entropy of a quantum circuit of Hadamard gate and a loop

The following Q&A about reversible computing is available here. It has listed a number of practical scenarios where a reversible circuit can still be dissipating heat. Let's assume that none of ...
0
votes
2answers
35 views

What are the hypothetic cases when entropy of a closed system may decrease? [on hold]

What are the hypothetical possibilities that entropy of a closed system may decrease? I would accept plausible but hypothetical setups. For instance, Non-trivial timeline topology (closed timelike ...
5
votes
1answer
312 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. ...
3
votes
4answers
2k views

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? ...
1
vote
0answers
50 views

Quantum Entropy-a minimization problem

I came upon this (not homework) problem of minimizing the following expression ...
4
votes
3answers
266 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 ...
0
votes
0answers
31 views

Deriving an Expression for Helmoltz free energy

Given the equations of states for an isolated system: $$E=\frac32 pV$$ $$p=aVT^4$$ I was asked to find the Helmoltz free energy per particle, $F=E-TS$, as a function of $T$ and $V$. I began with the ...
10
votes
1answer
498 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 ...
6
votes
2answers
116 views

Was the Big Bang actually cold?

As I understand, from watching the Discovery Channel, the total amount of energy in the universe is zero. As such, people like Hawking explain that the universe can be created out of nothing ...
3
votes
5answers
407 views

Integrating factor $1/T$ in 2nd Law of Thermodynamics

How would you prove that $1/T$ is the most suitable integrating factor to transform $\delta Q$ to an exact differential in the second law of thermodynamics: $$dS = \frac{\delta Q}{T}$$ Where $dS$ is ...
2
votes
1answer
106 views

H-theorem and Boltzmann equation applied to Boltzmann distribution

Using the Boltzmann equation: $$ \frac{dH}{dt} = \int_0^{\infty} dr \int_0^{\infty} ds W(r,s)[p_r - p_s][\ln{p_r} - \ln{p_s}],$$ and assuming $p_r = e^{-\beta r}$, the equation looks like $$ ...
15
votes
5answers
771 views

What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
0
votes
0answers
27 views

Is entropy related to Poincare recurrence time?

One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after ...
1
vote
2answers
80 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 ...
0
votes
1answer
49 views

Unmixing of gases: What is the relevant temperature for my Entropy?

This answer to a question about unmixing gases states: However, let us now assume we have to hand a source of mechanical work, and a large heat reservoir at temperature $T$. I'll assume that ...
1
vote
2answers
81 views

second law of thermodynamics

I'm a high school rookie learning thermodynamics right now by myself. I got really confused that the second law of thermodynamics states that the entropy of the universe is always increasing. If the ...
5
votes
2answers
104 views

How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
0
votes
1answer
30 views

Why do you want to maximise the entropy when deriving Boltzmann's distribution?

I am sure this has a simple answer, but I can't seem to get my head around in at the moment. I am going through the derivation of the Boltzmann distribution through maximising entropy through the ...
0
votes
0answers
30 views

The relationship between the two statistical mechanical definitions of entropy

It seems like similar questions have been asked here; hopefully my question is not a duplicate. I am reading my textbook on the statistical mechanical definitions of entropy, and I am very confused ...
2
votes
1answer
83 views

Death by entropy

An idea struck me as I was walking to class today. According to Wikipedia, entropy is defined as the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a ...
2
votes
1answer
119 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 ...
3
votes
2answers
3k views

Are reversible adiabatic processes always isentropic?

If my understanding is correct, neither reversible nor adiabatic processes are necessarily isentropic. But are reversible adiabatic processes always isentropic?
5
votes
3answers
1k views

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 ...
4
votes
2answers
98 views

What is the connection between the non-reversibility of the decay of unstable nuclei (as Uranium, Plutonium) and the 2nd principle of thermodynamics?

The 2nd principle of the thermodynamics says that if a system (e.g. an ideal gas) is left undisturbed, its number of microscopic states only increases. This is a statement of irreversibility of the ...
4
votes
1answer
92 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 ...
19
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 ...
0
votes
2answers
31 views

Entropy of ideal gas with finite volume

I know that the entropy of an ideal gas is given by the Sackur-Tetrode equation, but is there also a way to take into account that even the ideal gas will acquire some volume $v_0$? Or is it then just ...
1
vote
3answers
64 views

Comparison between entropy and internal energy

Why is entropy change a better way of determining a spontaneous process compared to the change in internal energy?
1
vote
2answers
275 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 ...
1
vote
2answers
75 views

Second Law from Statistics

Hi all I hope you can help me with the statistical origins of the Second Law. I cannot find anything that mathematically proves that order from disorder is impossible only improbable Leading me to ...
3
votes
2answers
73 views

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 ...
4
votes
2answers
177 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
0answers
55 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
1
vote
2answers
43 views

Entropy-A question. [closed]

If I have 100 coins then a macrostate is how many heads/tails I have, a micro state is the facing of each individual coin of the 100, but what then is a "configuration" in this example? It is a basic ...
8
votes
2answers
246 views

Why does $S = k_B \ln W$ not always apply?

I thought for a long time that the Boltzmann formula for entropy, $S = k_B \ln W$, was a universally true statement, or rather the definition of entropy from the perspective of statistical mechanics. ...
2
votes
1answer
577 views

Equation of state of a rubber band

I have the following question that I attached in png format. I have done part (a), but I am having difficulties in part (b) when I proceed according to the book. I have non zero tension at ...
1
vote
0answers
33 views

Entropy of this system

We have a system with two energy states $E_0$< $E_1=0$. We also know that state $E_0$ can only take at most $m$ particles. Curently, there are $n<m$ particles in $E_0$. Now, I am supposed to ...
0
votes
1answer
36 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 ...
11
votes
5answers
280 views

How does dark matter collapse?: Entropy considerations

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 ...
5
votes
4answers
130 views

Definition of Entropy in thermodynamics

In most textbooks, the definition of entropy in reversible processes on a system $S$ is given simply as $$d S=\delta Q/T.$$ It seems to me this definition is insufficient since it does not specify ...
1
vote
0answers
48 views

Can any one solve this integral equation? [closed]

I am presently working in the area "entanglement entropy". When i am trying to solve the integral equation $$\int_{-\infty}^{+\infty} dx_2' \rho_{2}(x_2, x_2') f_n(x_2') = p_n f_n(x_2)$$ for ...
3
votes
1answer
65 views

Why doesn't a Brownian ratchet provide free energy?

A Brownian ratchet is described here at Wikipedia. The "why it fails" section reads: Feynman demonstrated that if the entire device is at the same temperature, the ratchet will not rotate ...
4
votes
1answer
63 views

Imaginary time is to inverse temperature what imaginary entropy is to …?

The Wick-Rotation rotates imaginary time into inverse temperature (as can be seen from its "rotating" the Schrödinger equation into the heat equation). Now since entropy is temperature's conjugate, I ...
31
votes
7answers
3k views

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 ...