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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Estimate correlation function by information in the subsystems

Motivation $\newcommand{\expect}[1]{\langle \hat{#1}\rangle}$ Let me start with thoughts I had so far; there is a TLDR with my question at the bottom. Imagine a pure system $\rho$ and with a bipartite ...
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Entropy Change - which formula to use?

I am looking at a system of two solids A and B, that is isolated. A is at a higher temperature; thus, we have heat transfer from A to B. If I wished to calculate the entropy change: $$\Delta S_{tot} = ...
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Heat transfer from, or to, a large heat reservoir is always reversible?

A heat reservoir (Figure above) is a constant temperature heat source or sink. Because the temperature is uniform, there is no heat transfer across a finite temperature difference and the heat ...
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In a reversible heat exchange, does the system and reservoir need to almost have the same temperature?

In order for a process which involves heat flow from surroundings to the system to be reversible, is it necessary that the temperature difference between the system and surroundings be very small at ...
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Minimum energy principle for stars

In Townsend's Black Hole lecture notes, he says that at equilibrium, $E = E_{grav} + E_{kin}$ is a minimum, where $E_{grav}$ is the gravitational potential energy $-\frac{GM^2}{R}$ and $$E_{kin} = nR^...
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Is $C _v=T\left(\frac{\partial S}{\partial T}\right)_{V}$ true irrespective of reversibility of the process?

Without specifying if the process is reversible or not my textbook uses the relation $C_{V}=\left(\frac{\partial Q}{\partial T}\right)_{V}=T\left(\frac{\partial S}{\partial T}\right)_{V}$ Is this ...
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Could a Szilard engine power a car?

Is it possible to scale a Szilard engine up to the point of being able to power everyday things like cars, and if so what might a practical version look like? My understanding is that Szilard engine ...
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What does “entropy” really mean?

I'm currently taking a course of introduction to biophysics in college and we currently covered a subject called entropy (S). We did some maths based on the Carnot cycle and came up with the following ...
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Why $C_p=C_v$ for incompressible substances?

I'm learning entropy change for incompressible substances and on the way I saw this equality of $C_p=C_v$. I can't seem to understand this equality and I'm not able to visualize any such example. My ...
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How to calculate the overall entropy when continuous 2D positions are known?

If I have the positions of particles in continuous 2D space, how do I calculate the entropy of the system? The particles are invariant, I just need some measure of how organised they are, but I'm not ...
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Definition of quantum information, please!

I've been using the phrase "quantum information" for some time, but am beginning to wonder if the phrase means the same thing to me as to the QM community. Specifically, my understanding is ...
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Adiabatic expansion and energy spreading

I think of entropy as energy spatial spreading, but i find that in adiabatic expansion there is energy spreading but entropy does not increase. Is the internal energy decrease a way of energy ...
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How do I properly partially differentiate with constant $p$ in thermodynamics?

I'm trying to solve the following problem: a one component system is described by the following equations $$U=\frac{A^2}{4}NT^2\exp \left(\frac{V^2}{N^2}\right),\qquad p=T^2f(v)$$ where $v = \frac{V}{...
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Infinitesimal Changes - Notations

in my thermodynamics class we saw the following formulas: $$ dS = \frac{\delta Q}{T} $$ and $$ \delta W = PdV $$ This was part of a review of thermodynamics that we have seen previously; however, in ...
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Why does the Clausius inequality say entropy is closed cycle < zero?

I am not understanding how can clausius inequality say (closed)$\int{\frac{dQ}{T}}<0$. How does this not violate the second law? In closed cycle, entropy of a system should be either zero or ...
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How natural is the number $e$?

The definitions of Shannon entropy and Thermodynamic entropy bear a close resemblance to each other. Trying to take the analogy further we see that, in the definition of Shannon entropy, the base of ...
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Are the Rényi entropies mutually orthogonal over density matrices

For a density matrix $\rho \in D(\mathcal{H})$, the quantum Rényi entropy is defined as $$S_α(\rho) = \frac{1}{1-\alpha} \log \mathrm{tr}(\rho^\alpha), \alpha \in (0,1)\cup(1,∞)$$ Does it satisfy the ...
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Is the increase of entropy a theorem?

Let us consider an isolated system of $N$ particles whose motion is determined by Newtonian mechanic, over time that stretches from $-\infty$ to $+\infty$. The system is isolated, therefore the only ...
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How are these two statements about entropy at zero temperature mutually compatible?

Third law of Thermodynamics states that entropy of a system is zero at 0 Kelvin. When universe attains maximum entropy (Heat death), it will also approach 0 K temperature.
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Pure states as a proof entropy is emergent [closed]

Since the entropy of a pure state is zero, and assuming pure states are the most fundamental states i.e., there are no further levels of abstraction or building blocks, does this mean entropy is not ...
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Calculating entropy change

Entropy is a state variable, i.e. the data about the initial and final states would suffice to define change in entropy . However, while applying the formula dS = integral of dQ/T, I have distinctly ...
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Reversible vs Irreversible process

A Hypothetical Situation: Two thermally isolated identical systems have heat capacities which vary as: $$Cv =βT^4$$($β$ is constant) Initially one system is at $300K$ and the other at $400K$. The ...
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What is a fundamental force behind entropy?

There are four fundamental forces in the universe. They are behind every interaction in the nature. For instance, the electromagnetic force is behind friction. I wonder which fundamental force is ...
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I have problem understanding entropy because of some contrary examples

In many places over the Internet, I have tried to understand entropy. Many definitions are presented, among which I can formulate three (please correct me if any definition is wrong): Entropy = ...
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Entropy production associated with photon emission event

Consider a generic N-degree-of-freedom quantum system with equally spaced energy levels ($\Delta E = \hbar w$) described by the Hamiltonian $H=\sum_{n=0}^{N-1} n\hbar w|n\rangle \langle n |$. This ...
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Confusion regarding temperature and entropy

In my thermodynamics/statistical mechanics book ("Concepts in thermal physics", Blundell), the temperature of a system A has been defined as being one over the derivative of the entropy of A ...
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When does a hard drive have the most entropy?

Entropy is a measure of disorder, the higher the entropy the greater the disorder. Uniform systems have less entropy than random systems. Data is expressed in binary in computers, expressed as ones ...
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Maximizing the entropy with the density operator in QM [closed]

I am following Sakurai's (and Napolitano's) Modern QM, Section 3.4. I want to maximize the entropy $S=k\sigma$ by maximizing $$ \sigma=-\sum_k \rho_{kk}\ln\rho_{kk}~~, $$ where $\hat\rho$ is the ...
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Derivation of general equation of heat transfer & entropy

In Landau & Lifshtiz Volume 6 on fluid mechanics we derive the general equation of heat transfer by starting with the expression $$ \partial_t \left( \frac{1}{2} \rho v^2 + \rho \varepsilon \right)...
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Can thermodynamics be considered logical?

One of the laws says that heat won't flow from cool to warm and at the same time this same theory claims that there is a finite (albeit tiny) chance that it will, because there is always such a ...
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Which results in greater net entropy production: Building a house or skyscraper? [closed]

I'm trying to understand how entropy relates to the generation of complex systems. My understanding is that entropy refers to (edit: something proportional to the inverse of the) number of constraints ...
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Energy in ideal gas in isenthalpic process

In an irreversible isenthalpic process, where does the energy of ideal gas go? Since the temperature remains constant and pressure drops accompanied by an increase in entropy, is there any expression ...
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I need help in understanding why the entropy of the system does not change

I am studying heat and thermodynamics by zemansky. In the chapter entropy, there is a statement under the section 'Entropy and Irreversibility'- In the case of any process involving the isothermal ...
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Do we have entanglement measure in continuous variables (Not witness)?

I have been searching for entanglement measures for continuous variable systems like we have entanglement entropy for discrete variable systems. My searches have ended in entanglement witnesses. I was ...
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Entropy of electricity and heat

Is it correct to say that a MW hour of electrical energy delivered has less entropy than a MW hour ( 3.6 GJ) of process heat delivered, for example, in the form of steam?
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Proving that Entropy change of the system become zero for quasistatic process

Suppose a body with initial temperature to be, say $T_0$ and it cooled down to temperature $T_f$ (say) by contacting it to series of heat baths. I want to show that in the limit when heat baths become ...
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Time derivative of Gibbs entropy (the paradox of the constant fine-grained entropy)

In the context of classical systems, the fine-grained (or Gibbs) entropy is defined as the functional: $S_G(t)=-k\int_{\Gamma_t}dqdp\ \rho(p,q,t)\ln[\rho(p,q,t)]$ (1) I've been told (Wehrl and J. van ...
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“Equations of motions” and direction of maximal entropy

Say one has a system of statistical physics whose entropy is given as a function of one or multiple variables; for example as $S(x)$. An example of such a system could be a osmosis system, or a ...
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Phase Transition and changes in entropy

In the case of a Van der Walls gas where I could say that $S = C_v \ln(T) + R\ln(V - b) + cte$, noting it is stated on "Concepts in Thermal Physics" of Blundell: Note that the entropy ...
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Phase transition and Entropy

I know that in a phase transition, for example, to change from phase 1 to phase 2 at a constant temperature $T_c$, we need to supply some extra heat -- latent heat -- $L = \Delta Q_R = T_c (S_2-S_1)$...
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Black body radiation and second law

I'm struggling on finding what's wrong with my model of the following system which seems to break the second law: Imagine two punctual perfect black bodies at two temperature $T1 $ and $T2$. Each ...
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Calculate Entropy from pressure and energy

It's given that for a particular special gas, the pressure and the energy is given by, $ \begin{aligned} P &=\left(\sqrt{\frac{N}{V}}\right) \frac{T^{2}}{A} \\ E &=2 \sqrt{N V} \frac{T^{2}}{A} ...
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Calculating entropy of a cycle consisted of isothermal, isobaric and adiabatic processes

In a thermodynamic cycle, consisted of three processes: isothermal, isobaric and adiabatic, where all processes are reversible: Is it possible to show that change of entropy in the cycle is zero, ...
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Why only reversible adiabatic processes are called isentropic and not irreversible ones?

For both reversible and irreversible adiabatic processes, $dQ =0$,and by the definition of entropy $dS=dQ/T$, it should imply that entropy is constant for both. Why it is not so?
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Entropy and Irreversibility

I was watching Tenet and it made me think about some old questions I have. The second law of thermodynamics states that in every thermodynamics process, the variation of the entropy of a closed system ...
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Entropy reducing power generator

An 8.3 EER 1200 W air conditioner will move 10000 BTU of heat per hour. 1 BTU is 1055 J of heat. Per second this is moving 2930 W of heat energy. It is possible to get them even more efficient e.g. ...
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Are the thermodynamical laws extra fundamental interactions beyond the 4 fundamental interactions?

The four fundamental forces or fundamental interactions are Gravity Electromagnetism Weak interaction Strong interaction On Wikipedia, they are described as the interactions that do not appear to ...
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Adiabatical accessibility of gas unmixing

Consider a thermally insulated system, made of a room divided by a barrier into two compartments, each one containing an ideal gas at the same temperature. Call this the state $X$ of the system. If we ...
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Entanglement entropy inequalities for a sum of wavefunctions

I am learning about entropy in quantum mechanics, and I am trying to develop some tools and intuition. One tool that I have found very helpful has been $$\sum_{i=1}^k \lambda_i \mathbb{S}[\rho_i] \...
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Why does an increase in thermal energy lead to an increase in entropy?

After reading The Preference for Low Energy States, where it is stated in the excellent accepted answer that As macro states with a lot of energy stored in heat (our ball with random thermal motion ...

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