# 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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### Validity of the fundamental thermodynamic relation

I often read in engineering books that the fundamental theorem of thermodynamics $$dU=TdS-pdV$$ is valid for integration along reversible paths. Some considerations of mine (down below) led me to ...
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### How to prove that every reversible process must be quasi-static?

Using the definitions provided below, how do we formally show this for an in general open system? A quasi static process is a process in which the system is in constant internal thermodynamic ...
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### Book recommendations on measures of entanglement

I am an undergrad. physics student writing my bachelor thesis at the moment. What book would you recommend that talks about measures of entanglement? It would be really cool if it gave different ...
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### How can we calculate the change in entropy of a block and its surroundings, when the block is placed in a heath bath?

Let's say we have a block of lead (of heat capacity $C$) at temperature $T$, and a heat bath of temperature $T_0$. The block is placed in the bath and it cools to $T_0$ (a clearly irreversible process)...
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### One-body entropy?

In theoretical studies of Bose-Einstein condensates, it's common to look at the one-body density matrix: $$n_{ab}=\langle\hat{c}_a^\dagger\hat{c}_b\rangle$$ where the $\hat{c}_j$ are annihilation ...
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### A spontaneous exergonic reaction produces a reduced entropy structure and therefore constitutes a local entropy dip?

Total entropy of the isolated system increases due to release of work/energy, but locally, given that implicated elements are now bound together, entropy is reduced? We can assume low temperature and ...
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### Thermodynamics homework question - entropy [closed]

Below is a homework assignment question that I am gaving some trouble with. Firstly I don't understand what is meant by the explanation of the 2nd beaker, If I am to have an infinite series that ...
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### Help with 2nd Law and irreversibilty

This question is about the seemingly idealized notion of isolated systems and truly irreversible processes in the context of the 2nd Law. Here are the definitions and citations I'll use then my ...
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### Entropy as a state function for irreversible paths

Searching Physics Stackexchange for entropy I have found several posts regarding entropy, lately most of the questions why entropy is a state variable. This got me thinking. I have understood so far ...
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### Entropy as a state function - Is it just a postulate of the second principle?

I read quite a few questions on this website dealing with the idea of demonstrating that entropy is a state function. None of the answers I read seemed to be fully conclusive. So my question is : is ...
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### Entropy generation at the molecular level in a irreversible process

When we expand an gas irreversibly in an adiabatic process then there is intermolecular friction, but what exactly gets transferred to heat. I have read that the directed motion gets randomized. But ...
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### $\oint{A}=0\implies$ A is a State function?

If $A$ is a thermodynamic variable (ex:Pressure, volume, entropy). then If $\oint{A}=0$, then does it imply that $A$ has to be a state function? I'm trying to prove that Entropy is a state function. ...
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### Proof for $\oint \frac{dQ}{T}=0$ in a reversible process

I'm actually trying to prove that Entropy is a state function. I get struck at the point where I need to prove that $\oint \frac{dQ}{T}=0$ for a reversible process. Clausius in his book The ...
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### Formally define temperature as derivative of max gibbs entropy?

This question asks whether we can define the temperature in terms of the Gibbs entropy in the case of the canonical ensemble. In this question I want to ask whether we can define temperature in terms ...
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### Temperature dependence of entropy

$$\text{Entropy}=\frac{\text{Heat absorbed}}{Temperature}$$ $$\Rightarrow S=\frac{Q}{T}$$ $$[S]=[ML^2 T^{-2} K^{-1}]$$ If entropy increases with increase in temperature of the system, then it ...
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### Entropy change in a reversible and Irreversible path

Let's consider 2 cases. First where a system is taken from state 1 to 2 in a reversible path. Second where the same system is taken from state 1 to 2 in an irreversible path. Can we say that Entropy ...
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### Is Clausius' inequality a statement of the second law of thermodynamics?

From the Kelvin and Clausius statements of the 2nd law we can prove Carnot's theorem (no engine is more efficient than a heat engine), and this therefore becomes an additional statement of the second ...
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### Can life decrease the entropy of an isolated system? [closed]

A high entropy isolated system is shuffling through its more probable micro-states. Local entropy dip produce several structures. These structures, akin to life, feed on free energy to preserve ...
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### Is entropy $S$ a fundamental quantity like Temperature?

What I'm trying to say is that $$S=\int\limits_{T_1}^{T_2}\frac{\mathrm dQ}{T}\tag{1}$$ depends only on the initial and final states. Why is that so? Is it like a "law" (like Newton's law of gravity ...
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### Additional resources to Landau's approach to entropy

I extensively studied thermodynamics but was never really satisfied with how entropy is treated in this theory. Some time ago I started reading Landaus statistical physics. I find most of the book ...
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### Does the Big Bang have the absolute lowest amount of entropy? [duplicate]

We know that the event of the Big Bang has low entropy (and we don't know why), but... do we know for certain (or through convincing mathematical evidence) that the event of the Big Bang indeed has ...
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### Entropy and Competition [closed]

Is there any particular reason why entropy cannot be considered to be a measure of or proxy for the level of competition in a system? Take a system of competitive or cooperative agents (human, ...
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### Time rate of thermodynamic potentials

In equilibrium thermodynamics we're concerned with the change in thermodynamic potentials between two equilibrium states (e.g. $\Delta U$, $\Delta G$, etc.), and we use these changes to make ...
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### Calculating entropy in truncated Wigner

I'm trying to get some reasonable measure of the entropy of a system modelled by the truncated Wigner method. The Wigner function contains all the information about a density matrix. So, I figure it ...
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### Calculate entropy of a sphere (?)

I saw these two videos (1 and 2) and in both of them Tony Padilla gives basically the same definition of maximum entropy in a region of space (a sphere). Now, searching the web I haven't found any ...
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### Why is entropy maximal under $(U,V)$ constraint? Construction of maximal entropy at equilibrium from thermodynamic potential

Let us consider a system exchanging work via pressure force only. It is assumed to be at mechanical equilibrium with the environment. We can write down the differential of the thermodynamic potential ...
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### Is entanglement a bulk property or surface property?

The degree to measure entanglement in a many-body system is entanglement entropy. There are different measures for entanglement entropy, for example, Von Neumann entanglement entropy and Renyi ...
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### Uncertainty of wave function over time [duplicate]

If entropy is the amount of randomness in a certain system, and it has to increase, by the second law of thermodynamics, does that mean that the uncertainty of the state of a particle always increases ...
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### Second law of thermodynamics less intuitive [closed]

The zeroth and first laws of thermodynamics seem like common sense but the second law is not very intuitive- how can someone think of ' the entropy of the universe is always increasing'? Shouldn't ...
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### How can you (computationally) calculate the halfchain entanglement entropy of a spinchain?

I am simulating a (small) spinchain with exact diagonalization and dynamics. I would like to track the entanglement entropy of half the chain with the other part of the chain. I have the vectors of ...
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### Generalised basis independent relationship between Von Neumann Entropy and Purity of a quantum state [duplicate]

I have been trying to find a generalized relationship between Von Neumann Entropy and Purity of a quantum state? In this post there is a discussion of a specific case for a qubit and a more general ...
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### What do the phrases “connected therewith” and “direct contact” in Clausius's law mean?

I have questions about Clausius's law. The specific questions are: 【My Questions】 (1)What and what is connected in “connected therewith” in 【Quote 1】 below? (2) Give me some specific examples of "...
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### Would entropy maximized at equilibrium if there were no irreversible processes? [closed]

I have read this question, but it does not answer my question: In a truly ideal isolated system (say an ideal gas), it is quite possible that there is no irreversible process such that the net ...
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### How should I interpret this thermodynamic inequality?

I'm a little bit confused over the following inequality: $$dS > \frac{\delta Q_{irrev}}{T}$$ An infinitesimal change in entropy is defined in this way: $$dS = \frac{\delta Q_{rev}}{T}$$ ...
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### Confused with Entropy and Clausius inequality

I am confused with a question in my thermodynamics class and would like to seek some clarification. The problem I was given: A reversible heat engine operates on a Carnot Cycle between a heat source ...
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### Heating of Water, Reversible/irrevserible process

I'm hoping that someone can help me understand this problem. I am determining which of these processes are reversible and irreversible. If we had some beaker of water at room temperature which came in ...
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### Is it possible to deduce the second law of thermodynamics from the first?

Considering the First law of thermodynamics as an axiom dU=dQ-pdV for any infinitesimal process, we should be able to prove that for any reversible(quasistatic) and cyclic transformation, there is at ...
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### Quantum System with Only One Energy Level

Is it possible for a quantum system to have a maximum energy level. And, is it possible for that maximum energy to also be equal to the ground energy? Let's assuming such a system can exist. What ...
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### Does the Casimir effect violate the Generalized Second Law of Thermodynamics?

In order to avoid violation of the Generalized Second Law of Thermodynamics by classical non-minimally coupled scalar fields, Ford et al demonstrated that the quantum inequalities prevent the negative ...
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### Should entropy be always extensive?

My question came up from the discussion in class which is about whether we should treat a specific system distinguishable or indistinguishable. To figure out what will happen in these two ...
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### Change in entropy of an iron bar [closed]

A small iron bar of mass $M = 1kg$ at temperature $1000 K$ is put in a lac at temperature $288 K$. Given that the thermic capacity of the iron bar is $440 J \cdot kg^{-1} \cdot K^{-1}$ I need to ...
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### Thermodynamic entropy and energy required for measurement

In the framework of information entropy, one common question is how to develop a code that minimizes the cost of transmission of a message, given that each bit as a fixed unit price. If the ...
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### Why does the minimum energy principle work?

The principle of minimum energy states that in a thermodynamic system the equilibrium state corresponds to the minimum energy state among a set of states of constant entropy. I believe I understand ...
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### Is entropy conserved in an isolated system with two containers of gas separated by a diathermal wall at different initial energies?

Question is pretty much the title. If I take a system of two gases and allow them to exchange heat I can write the total entropy as $$S_{total}=S_A+S_B=k_b(\ln{\Omega_A+\ln{\Omega_B})}.$$ Will ths ...
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### Does entropy depend on reversibility?

When going through a cycle of a process $A \rightarrow B \rightarrow A$, is the change in the entropy of the system always equal to $0$? Does the reversibility of the process change anything (done ...
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### Does the wave function decay? [closed]

Does the wave function decay? Is the wave function subject to entropy? Does a particle decay while it's in superposition or does decay start when a measurement occurs?
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### Contradiction in definition of entropy?

I'm studying for my thermodynamics exam and I came across something which really confuses me. An infinitesimal change in entropy $dS_{sys}$ of a system at temperature $T_{sys}$ during a reversible ...
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### How does entropy help decide the spontaneity of a reaction?

Consider the endothermic reaction: $$2\ CH_3COOH\ (l)+(NH_4)_2CO_3\ (s) \to CH_3COONH_4\ (aq)+CO_2\ (g)+H_2O\ (l)$$ This reaction is spontaneous despite being endothermic because the entropy change ...