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 the change of entropy in the Universe?

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 this paper, Wald related the black hole entropy to the Neother charge using the covariant phase space formalism. In proving this relation, Wald noticed that on the bifurcation surface, the Killing ...
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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 ...
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When heat flows from hot to cold, do individual particles share energy or is it just a statistical effect?

I'm struggling to get a clear understanding of why heat flows from hot to cold. I understand that temperature reflects the average kinetic energy of the particles, and that kinetic energy transfers ...
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Interpretation of change in entropy and how to formulate an expression for how much energy required to mix gases.?

From statistical mechanics one cab derive the change of entropy of the mixing of two ideal gases with the result $$\Delta S_\text{mix} = - n R \Sigma_{i} x_i \ln(x_i)$$ where $n$ is the total amount ...
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Entropy function additivity

I am reading Herbert Callen's book Thermodynamics, which proposes a postulatory treatment to the subject. The postulate number 3 states the properties of the "entropy" function, one of which is the ...
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Would the Earth have weighed the same if no life had developed on it?

I was reading this question and talking about it with my flatmate when a question came up. Ignoring the effects of losing or gaining mass due to cosmic dust, meteorites, and atmospheric losses as ...
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Need verification for the entropy equation in statistical thermodynamics

The relationship between entropy $S$, the total number of particles $N$, the available energy levels $E_j$ and a yet to be defined parameter $\beta$ is: $$S(\beta)=k_B \cdot N \cdot \ln\bigg(\sum_{j=1}...
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Information content in black holes

Bekenstein-Hawking formula for entropy of a black hole tells us that information content in a black hole is proportional to its area which is in fact proportional to the mass^2 of the black hole. The ...
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If all spacetime paths inside a black hole point towards the singularity, then does that mean entropy is decreasing?

Entropy is a concept of disorder. A drop of blue ink inside a glass of water only has 10^10 factorial possible ways of being an ink drop, but it has 10^11 factorial possible ways of being an ink soup. ...
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Amount of particle collisions depending on entropy

I'm doing a very simple simulation of random particles. Simple mechanics, elastic collisions. (The simulation is based on a next-event time progression.) When I count the number of particle particle ...
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The relationship between time, relativity and entropy

I came across a discussion about the nature of time and whether or not time is an illusion on a physics forum. I'm not so much interested in the philosophical issues regarding time, but the following, ...
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Regarding the Boltzmann entropy formula, is the Boltzmann constant really arbitrary?

In the top answer to this question (Is the Boltzmann constant really that important?) I read that the Boltzmann constant is just a dummy factor which converts energy to temperature. But that allows ...
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Entropy, Thermodynamics and Information

This is a bit of a shower-thought, so forgive me if it is ill-conceived or a stupid question! It occurred to me that, to preserve information, you need to use energy. For example, say you have a book ...
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Minimal work required to produce ice at room temperature

I'm wondering about the most efficient way of producing ice from water at room temperature. First of all: why, in principle, do we need to put in work to do so, if water gives off energy while ...
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Heat transfer reservoir and system at same temperature

I just read that "a heat transfer between a reservoir and a system at same temperature is a reversible process". If there's no temperature difference, why would there be a heat flow?
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Entropy density (entropy per particle)

How I can get this definition for an ideal gas: $s=C v \ln (Pρ^{−\gamma})+ \text{constant} $ ? In this answer it is mentioned that there is a connection with the Sackur-Tetrode relation of the ...
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What is the difference between fine-grained and coarse-grained entropy?

So I am not a native English speaker, but I understand the words "coarse" and "fine" grained. But I really don't know what to make of them in the context of entropy. I have encountered this many times ...
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How to solve the equation of motion of the minimal surface for spherical subsystems in AdS?

In order to compute the holographic entanglement entropy for a spherical subsystem in AdS using the Ryu-Takayanagi conjecture, one needs to solve the following second order nonlinear differential ...
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Variation of entropy with volume under constant pressure

For a thermodynamic system defined with E and V (internal energy and volume), how would the entropy vary with the volume, under constant pressure? I've managed to get dS = Cp * ln ( T2 / T1) , where ...
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Superoperator cannot increase relative entropy

So I have to show that a superoperator $\$$ cannot increase relative entropy using the monotonicity of relative entropy: $$S(\rho_A || \sigma_A) \leq S(\rho_{AB} || \sigma_{AB}).$$ What I have to ...
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What happens to the electronic movements at absolute 0?

what happens to the motion of electrons in the their respective orbits when a substance is cooled down to zero kelvin? assuming they stop moving then are they gonna stick to the nucleus? if yes what ...