Entropy Definition and 999 Threads

In his classic textbook, Callen remarks that I have labelled the claims (1) and (2). I am not sure about either. For the first, I have tried to proceed as follows (all equations are from Callen's second edition and all 0 subscripts are with respect to some reference state of an ideal gas): I...

In Chapter 5 of his famous textbook on thermodynamics, Callen argues for the "equivalence" of the maximum entropy (Max-Ent) principle and the minimum energy (Min-En) principles. I quote from Callen first: As far as I know (though Callen never makes this explicit in what, I think, represents...

I am continuing to try to understand maximum work reversible processes (and a subset thereof -- Carnot cycles) better. I am here curious about the following system. My question is about how I can know/prove that there exists a way to take the gas (the primary subsystem) reversibly with respect...

This question was, effectively, asked here (please refer to that question for additional context); however, I don't think the given answer is correct (or at least complete) despite my having added a bounty and having had a productive discussion with the answerer there. In particular, I don't...

Hello everyone, I am seeking some clarification regarding a question related to thermodynamics and statistical mechanics. My understanding is that when we combine two identical boxes with the same ideal gas by removing the wall between them, the resulting system's entropy stays the same...

The Bekenstein Bound places a upper limit on the amount of entropy that a given volume of space may contain. This limit was described by Jacob Bekenstein who tied it quite closely to the Black Hole Event Horizon. Put simply, black holes hold the maximum entropy allowed for their volume. If you...

What does entropy in the following sentence means? Does it mean the same as the term "information content" before it? Is entropy more technical a term than information content? He remembered taking a class in information theory as a third-year student in college. The professor had put up two...

The starting point is the identity $$\left(\frac{\partial u}{\partial T}\right)_n = T\left(\frac{\partial s}{\partial T}\right)_n.$$ I then try to proceed as follows: Integrating both with respect to ##T## after dividing through by ##T##, we find $$ \int_0^T \left(\frac{\partial s}{\partial...

Dear everyone, I wish to discuss in this thread a classic/semi-classic interpretation on the origin of Bekenstein-Hawking entropy and the related resolution to Hawking's information missing puzzle, which were published in Nucl.Phys.B977 (2022) 115722 and Nucl.Phys.B990 (2023) 116171 after...

Hi everyone! It's about the following task: Calculate the molar entropy of H2O(g) at 25°C and 1 bar. θrot = 40.1, 20.9K, 13.4K θvib=5360K, 5160K, 2290K g0,el = 1 Note for translational part: ln(x!) = x lnx - x Can you explain me how to calculate this problem?

I would like to calculate the entropy or enthalpies (steam, specific and inner energy) using the SRK [suave-redlich-kwong] equation, the Wilson approximation and (if necessary) the Antoine equation. and the Clausius-Clapeyron equation for a mixture of 0.199 mol/l nitrogen and 0.811 mol/l carbon...

Hello, is someone able to explain why these two are wrong. I am not sure how to figure out the enthalpy direction as the reaction is not changing state of matter, nor is it changing temperature. (Please solve without calculating anything) Thank you

The FAQ by @bcrowell cites an explanation by physics netizen John Baez as to how entropy rises when a star loses heat and contracts. However, the linked explanation falls short of describing the key role that gravity must be playing. The FAQ by @bcrowell discusses why a low-entropy state of...

For this, I don't understand how we can apply the change in entropy equation for each solid since the ##\frac{dT}{dt}## for each solid will be non-zero until the solids reach thermal equilibrium. My textbook says that the ##\Delta S## for a system undergoing a reversible process at constant...

For this, Why dose they write the change in entropy equation as ##\Delta S = \frac{Q}{T}##? Would it not better to write it as ##\Delta S = \frac{\Delta Q}{T}##, since it clear that we are only concerned about the transfer of heat in our system while it remains at constant temperature as all...

In the book "Cycles of Time" by Roger Penrose, there is a part of the explanation of entropy that I don't understand. There are 10^24 balls, half of which are red and the other half blue. The model is to arrange the balls in a cube with 10^8 balls on each edge. It also divides the cube into...

In classical statistical physics, entropy can be defined either as Boltzmann entropy or Gibbs entropy. In quantum statistical physics we have von Neumann entropy, which is a quantum analog of Gibbs entropy. Is there a quantum analog of Boltzmann entropy?

I came across the following statement from the book Physics for Engineering and Science (Schaum's Outline Series). I cannot seem to find a satisfactory answer to the questions. Is the statement in above screenshot talking about entropy change the statement of Second Law of Thermodynamics or is...

Entropy question. Take a finite number of identical atoms in a specific volume of space at a moment of time. Run two thought experiments on this system scenarios (both time independent) 1: expand the volume of space of the system instantaneously by a factor of 10. The fixed number of atoms...

Unfortunately, I have problems with the following task For task 1, I proceeded as follows. Since the four bases have the same probability, this is ##P=\frac{1}{4}## I then simply used this probability in the formula for the Shannon entropy...

Two systems A & B (with orthonormal basis ##\{|a\rangle\}## and ##\{|b\rangle\}##) are uncorrelated, so the combined density operator ##\rho_{AB} = \rho_A \otimes \rho_B##. Assume the combined system is in a pure state ##\rho_{AB} = |\psi \rangle \langle \psi |## where ##|\psi \rangle =...

Hi, Unfortunately I am not getting anywhere with task three, I don't know exactly what to show Shall I now show that from ##S(T,V,N)## using Legendre I then get ##S(E,V,N)## and thus obtain the Sackur-Tetrode equation?

Hi, Unfortunately, I have problems with the task 4 In task 3 I got the following $$ T_f=T_ie^{\Delta S_i - c_i} $$ Then I proceeded as follows $$ \Delta S = \Delta S_1 + \Delta S_1 $$ $$ \Delta S =c_1ln(\frac{T_ie^{\Delta S_i - c_i}}{T_1})+c_2ln(\frac{T_f}{T_2})$$ $$ \Delta S...

I understand that S (Ssys) is a state function but I can't understand why Ssurr and Suniv (or Stot) are a path function.

For now it is only about the 1 task If the task states that: You can approximate that their dynamics in water resembles that of an ideal gas. Does it then mean that I can take glucose as the ideal gas and then simply calculate the entropy for the ideal gas?

For a freely expanding ideal gas(irreversible transformation), the change in entropy is the same as in a reversible transformation with the same initial and final states. I don't quite understand why this is true, since Clausius' theorm only has this corrolary when the two transformations are...

Summary: doesn't this decrease entropy ? Cellulose is known for its hydrophilic quality, which can be explained from the polarity of its hydroxyl groups. We all know water can overcome the force of gravity through a piece of paper you put in the water. Correct me if I'm wrong but this is a...

If you were to condense all the energy in the universe into a point, wouldn't the temperature be very high, yet the entropy be very low? Also if you were to spread out all of the energy in the universe, wouldn't the temperature be near zero and the entropy be very high? And this makes entropy...

Summary: Trying to understand the relationship between gravity, thermodynamics and entropy, thank you. Gravity can take a diffuse cloud of gas filling a given volume of space at equilibrium density and temperature, and turn it into a burning star surrounded by empty space. Does this mean that...

Christoph Schiller, "From maximum force to physics in 9 lines -- and implications for quantum gravity" arXiv:2208.01038 (July 31, 2022). This paper asserts that nine propositions can be used to derive the Standard Model and GR and can point the way to quantum gravity, although he cheats a bit...

Quantum gates must be reversible. The usual justification for this is that in QM the time evolution of a system is a unitary operator which, by linear algebra, is reversible (invertible). But I am trying to get a better intuition of this, so I came up with the following explanation: In order to...

Now, it's been said that the majority of the entropy in the universe resides within the cumulative entropy of black holes inside the universe. How do they know that? Now, I'm not so interested in how they determine the black hole's entropy, I know there's a relatively simple formula for that...

Boltzmann entropy definition is given by: $$ S = k_B lnW $$ where ##W## is the weight of the configuration which has the maximum number of microstates. This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...

In the definition of entropy, there are two. One is about the degree of randomness and one is about energy that is not available to do work. What is the relationship between them?

If the Universe could somehow reach a state of infinite entropy (or at least a state of extremely high entropy), would all fundamental symmetries of the physical laws (gauge symmetries, Lorentz symmetry, CPT symmetry, symmetries linked to conservation principles...etc) fail to hold or be...

I was reading about thermodynamics postulates when i came over the differnetial fundamental equation: I understand that the second element is just pressure and last element is chemical energy, but he problem is i don't understand what is the use of entropy and how does it contribute to a...

Hey to all,... It is now generally believed that information is preserved in black-hole evaporation. This means that the predictions of quantum mechanics are correct whereas Hawking's original argument that relied on general relativity must be corrected. However, views differ as to how...

Is there any approach in any books out there, where we consider that in universe exists only one field, let it be called the Unified Field (UF), in which all of the known fields (gravitational, EM field, quark field, gluon field, lepton field, Higgs Field, e.t.c.) are just components (pretty...

(a) We first find that: ##T_A=\frac{P_A V_A}{nR}=\frac{1\cdot 10^5 \cdot 4}{40\cdot 8.314}K\approx 1202.7904 K##, ##\frac{T_B}{T_A}=\frac{\frac{P_B V_B}{nR}}{\frac{P_A V_A}{nR}}=\frac{P_B V_B}{P_A V_A}=\frac{P_A \frac{V_A}{2}}{P_A V_A}=\frac{1}{2}##, ##\frac{T_C}{T_B}=\frac{P_C...

Hi Pfs, There are different kinds of entropies. I discoved the free entropy. https://arxiv.org/pdf/math/0304341.pdf the second law says that the total entropy cannot decrease when time goes by. Is it always the same "time" for the different entropies? the author, Voiculescu, wrote articles...

I am a software trainer and know about as much Physics as I've been able to pick up from the BBC‘s occasional documentaries. I have never even taken a physics course in high school or college so I am an absolute lay-person here with what’s probably a very lay-person question… I was watching...

I think the solution is: $$dU=\delta W_{prop}$$ $$dU=TdS-PdV$$ $$dV=0$$ then, $$TdS=\delta W_{prop}$$ and so $$dS=dU/T$$ and by the way, it correct to say that, if the transformation between the initial and the final state would happen in a reversible way then the heat transfer could be...

I have a rather general question about the definition of entropy used in most textbooks: S = k ln Ω, where Ω is the number of available microstates. Boltzmann wrote W rather than Ω, and I believe this stood for probability (Wahrscheinlichkeit). Obviously this is not a number between 0 and 1, so...

one of the claimed successes of string theory is its ability to derive the correct Hawking-Bekenstein equations to calculate the quantum entropy of a black hole without any free paramenters, specifically Extremal black hole entropy using supersymmetry and maximal charge. I was wondering if...

I have a question about the Thermodynamic Identity. The Thermodynamic Identity is given by dU = TdS - PdV + \mu dN . We assume that the volume V and that the number of particles N is constant. Thus the Thermodynamic Identity becomes dU = TdS . Assume that we add heat to the system (we see that...

Hello Sorry for my English... We approach slowly (in a quasi-reversible way) an electrical charge of a glass of salt water. Some ions arrange themselves in the glass. What can we say about entropy of this transformation? Bernadette PS: My reflection comes from reading an old physics book...

Let's say you have a very dirty small room room and a giant clean library (lots of organized books) and let's say these occupy the same number of microstates. The entropy according to this equation is the same for the library and the room. But one is more ordered than the other one. How does it...

In a certain thermodynamics textbook, specific work done by an isentropic compressor/pump in an ideal rankine cycles, is given by the following; Wpump = h2 - h1 Wpump = v(P2 - P1), where v = v1 When I carry out these two calculations between any two states, I get vastly different answers...

As we know, dipole can be only arranged either parallel or anti-parallel with respect to applied magnetic field ## \vec{H} ## if we are to use quantum mechanical description, then parallel magnetic dipoles will have energy ## \mu H ## and anti-parallel magnetic dipoles have energy ## -\mu H##...

So I am midway through my Thermodynamics course in college and still feel a bit unsure about the 2nd law and entropy. I've learned that the 2nd law was states 3 different ways, and by contrapositive proofs we can determine they are all equivalent. What we end up getting for the 2nd law is...