Questions tagged [entropy]

An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

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What is entropy change due to mass transfer?

Since entropy is an extensive property, it can change via mass transfer. But entropy change for internally reversible process is defined as $\int\frac{\delta Q}{T}$, which does not account for mass ...
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2nd law of thermodynamics inside an event horizon?

Since time and space switch roles inside a black hole, does entropy inside a black hole still need to increase? If not, maybe something very strange could pop into existence, only to be crushed ...
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What motivated Gibbs's definition of Gibbs entropy?

What motivated Gibbs's definition of Gibbs entropy? I have read and I think that I agree with the idea that if we have to choose probability distribution for an unknown system then it is a good idea ...
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Can some type of matter in its gas phase ever have lower entropy than another type of matter in its liquid phase?

I'm trying to deepen my understanding of entropy beyond the overly simplistic analogy with "disorder". Consider some matter in its gaseous phase that has been cooled to just above its condensation ...
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three particles on a state with negative energy have negative temperature?

Suppose three particles on a state with energy $-\epsilon$, that is, $H\lvert\Phi_1\rangle=-\epsilon\lvert\Phi_1\rangle$, as the average energy per particle is $kT$, but is also $-\epsilon/3$, wouldn'...
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is entropy the same up to a constant?

I have understood that what's important about entropy is its change $\Delta S$, not $S$ itself, much like the electrostatic potential. Therefore, can I assume that a constant entropy can be redefined ...
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Carlo Rovelli: “Is Time’s Arrow Perspectival?”

I came across a paper in which Carlo Rovelli argues that "the entropy we ascribe to the Universe depends on the peculiar coupling between us and the rest of the universe". Rovelli suggests that the ...
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Does the entropy of a system of two gravitating bodies increase as they get closer together?

It seems like the situation where the two gravitating bodies have collided and coalesced (assuming that they don’t shatter on impact) can be thought of as the ‘equilibrium’ of the system, since this ...
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Entropy change of the surroundings

My textbook says: $\displaystyle\Delta S_{surr}=\frac{q_{surr}}{T}=-\frac{q_{sys}}{T}$ So far, so good. It then goes to say: $\displaystyle\Delta S_{surr}=\frac{-\Delta H_{sys}}{T}$ [at constant $P$...
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Thermodynamic definition of entropy describing reversible processes

I've recently started learning about entropy. One possible definition is that it is the logarithm of number of microstates of particles. Another possible definition is that for a reversible (...
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Calculating entropy change in this irreversible process

A 15.0-kg block of ice at 0.0°C melts to liquid water at 0.0°C inside a large room at 20.0°C. Treat the ice and the room as an isolated system, and assume that the room is large enough for its ...
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What is the meaning of complex-valued entropy?

I was wondering, from Boltzmann Formula, $$S = k \ln{W}$$ where $k$ is Boltzmann's constant, what happens if $W$ is negative value. If $W$ is a negative value, then it can be rewritten as $$-W = e^{...
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Entropy change associated with loss of photon

I have a result with no reference which I hope to understand how this result is derived. Say the entropy change associated with the loss of a photon from the incident Bose field is $$ \Delta S = -K \...
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Entropic Restrictions to Water Interfaced with Hydrophobic Molecules

The occlusion of hydrophobic molecules from polar solvent such as water, I have read, is an entropic effect. My question is pretty simple -- at an interface of water and oil, or in the clathrate cage ...
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What type of energy should I use when describing the amount of energy available to increase entropy of a system?

There are many different specific definitions of energy within different physics fields: In thermodynamics we have at least U (system internal energy), F (Helmholtz Free Energy), G (Gibbs Free Energy),...
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Examples of a lower energy state being a lower entropy state?

I have heard that in quantum mechanics, the term "lower-energy state" is often used as a stand-in for a concept that should really be called "higher-entropy" state. There isn't a law that says that ...
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Can the universe be seen to have an information entropy of about zero?

I recently made some thoughts about fractals and especially how much information they carry. If we consider for example the Mandelbrot set, we can basically "find" an infinite amount of patterns at ...
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Entropy change in reversible and irreversible processes

$dS = dq/T$ for a reversible process and $dS \gt dq/T$ for an irreversible process, but why is the entropy change greater in an irreversible process? What difference between the two processes in ...
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Intuition on the overall entropy increase caused by heat transfer

Let's say that Hotter Gas A loses heat to Colder Gas B. Heat is transferred from A to B in such a way that the overall entropy increases. This can be proven with equations, but what is the intuition ...
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What is the change of entropy for a resistor at constant temperature?

A 10 Ω resistor is held at a temperature of 300 K. A current of 5 A is passed through the resistor for 2 minutes. Ignoring changes in the source of the current, what is the change of entropy in (a) ...
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Increase in entropy and integer factorization (How much work does one have to do to revert “irreversible” processes?)

This is not necessarily a direct physics question, but I am hoping, that by posting it here, someone can give a hint from the physics perspective. It is known, albeit not proven, that integer ...
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The Killing vector at the bifurcation surface of a stationary black hole

In the paper Black Hole Entropy is Noether Charge, Wald related the black hole entropy to the Neother charge using the covariant phase space formalism. In proving this relation, Wald noticed that on ...
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Do irreversible processes indicate that time reversible symmetry is a limited phenomenon instead of a universal law? [duplicate]

Physics and chemistry indicate various irreversible processes, while physics also proposes the theory of time reversible symmetry (T-symmetry). I suppose that evidence of irreversible processes ...
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A Spontaneous Reaction with greater ordering

I wanted to ask a question regarding entropy in a reaction. I was given the reaction $2H_{2}$ (g) + $O_{2}$ (g) $\rightarrow$ $2H_{2}O$ (l) and asked: the overall process is spontaneous but ...
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Max. Entropy = Min. Energy?

If a closed system has a submaximum entropy, then we can assume that in theory we can extract energy and thus the system goes to the maximum entropy state and no free energy is available. On the other ...
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Entropy in non-homogeneous equilibrium states and local thermodynamic equilibrium

My question concerns the possibility of using the hypothesis of local thermodynamic equilibrium for calculate the entropy of a non-homogeneous equilibrium states. For example, let's imagine the ...
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Does an information-theoretical approach proof the equivalence of total order and total chaos?

In the light of information-theory, are a state with maximum and minimum entropy the same? In the case of gas (maximum entropy), one needs very little words to describe a part of the system, which ...
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Does positive total entropy generation means that the entropy generation of the system and the entropy generation of the surroundings are positive too

When I was working on problems related to entropy generation, there was this problem that asks if the process claimed in the problem is possible or not. The solution manual calculated the total ...
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entropy and redundancy of data

I have a quick question about the redundancy of data and the information that it represents. A means of evaluating the amount of information contained in the data is evaluated with a notion of entropy....
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Expansion of Von Neumann entropy for small deviations

Suppose that your quantum system is described by $\sigma = \rho + \delta\rho$, where both $\sigma$ and $\rho$ are density matrices while $\delta\rho$ is "small". The Von Neumann entropy of the system ...
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Infinite entropy in ideal gas

Does it make sense that entropy goes to infinity as temperature goes to infinity? For an ideal monoatomic 1D gas I have an expression for entropy \begin{equation} S=Nk_{B}Ln(\frac{Ve^{\frac{5}{2}}\...
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Entropy generation of constant volume heat addition process

For an ideal gas constant volume heat addition process, change of entropy equation is: $$\Delta S= c_v \ln\frac{T_2}{T_1}+ R \ln\frac{v_2}{v_1}= \int \frac{dq}{T}+S_{gen}$$ The term $R \ln\frac{...
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Non-composable entropies

Being not at all a specialist of the subject my question is maybe naive, I apologize if it's the case. The question is the following: There are many different version of entropy functionals around (...
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Can Entropy Change be negative in this situation?

The temperature of two moles of an ideal diatomic gas is decreased from 𝟔𝟎𝟎 𝐊 to 𝟑𝟎𝟎 𝐊 at constant pressure. Is entropy change negative?
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Forecast in cosmology survey : loss or gain of information with cross-correlations

In the context of a forecast in cosmology, I am currently working on Fisher's formalism which is part of a more general theory, that of information. My problem applies to estimating cosmological ...
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A derivation in Jaynes' paper, linking stat-mech and Shannon's entropy

I have been going through E. T. Jaynes' 1957 paper, Information Theory and Statistical Mechanics. There is a step in his derivations, which has been giving me headaches for the past day; would ...
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Equality condition for relative entropy under partial trace

It is known that the relative entropy is non-increasing under arbitrary quantum operations. That is for some completely positive trace preserving map $N$, we have for all $\rho$ and $\sigma$ $$S(\rho ...
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Relation between maximally mixed state and thermal state

Hawking calculated the density matrix of the outgoing radiation to be a thermal state. I have heard people say this is a maximally mixed state. Is this because given a fixed average energy in the ...
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How can entropy always be increasing, while each microstate (among which low-entropy micro states) is equally likely to occur?

The reasoning in my statistical physics book is as follows: $\cdot$ The basic postulate of Statistical Mechanics is that for a system with a fixed energy, particle number and volume, each microstate ...
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Can anyone recommend a book on sigma phase?

I am looking for a book in Solid State Physics where I could find a systematic approach to sigma-phase (closed packed structures) and high-entropy alloys. So far, I have only found published papers on ...
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Why is the entropy production inside the system zero for a reversible process?

For a reversible process, why is the production of entropy within the system equal to zero?
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Why is that a system lowering its Helmholtz/Gibbs free energy must automatically have the same temperature as its environment?

Let's say we have a system in contact with a large reservoir. Let's also fix the number of particles in the system, as well its volume, so that the only thing that could be exchanged is energy. Now ...
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If entropy decreases for cold systems, isn't the heat death of the universe a state of low entropy? [duplicate]

Entropy is a consequence of heat. The heat death of the universe results in an approach to absolute zero temperature. Does this mean the end of the universe is low entropy?
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Is it there any relation between an action and entropy?

I've found papers that seem to suggest that these concepts are the same, like this one: https://arxiv.org/abs/1005.3854 But I've found answers in Physics Stack Exchange that say that both are ...
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How can an isolated system filled upto the brim with some fluid get more random? [duplicate]

This is probably stupid, but like an isolated tank which is completely filled with some liquid or stuff can't have any more entropy on its own right?
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Is there a definition for a *geometric entropy*?

In statistical mechanics, entropy of a system is usually defined as a measure of the system's micro-state randomness, or as an averaged "surprise" of its micro-state: \begin{equation}\tag{1} S_{\text{...
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Is it possible to determine configurational entropy of a material experimentally?

Configurational entropy is the entropy due to arrangement of atoms in a material. Is it possible to estimate it thorugh any experiment ?
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Is there a classical correspondence of the entanglement entropy in isolated quantum systems?

For an isolated quantum system, one can study the time evolution of entanglement entropy after a quantum quench (always a pure state), which has a rich behaviour in various different models. However, ...
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Value of $\beta$ in Boltzmann statistics when degeneracy of quantum states is taken into account

The relationship between entropy $S$, the total number of particles $N$, the total energy $U(\beta)$, the partition function $Z(\beta)$ and a yet to be defined constant $\beta$ is: $$S(\beta)=k_BN \...
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2nd law of thermodynamics for non-quasistatic processes

The 2n law of thermodynamics can be stated in terms of entropy as follows $dS \geq \frac{dQ}{T},$ which holds for all quasistatic processes (reversible and irreversible ones). Is there a ...