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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Change in entropy of engine and the hot bath in a cycle

I want to clarify that this question is not a homework-type question. I have provided its solution and the apparent discrepancy. This is a question from a national competitive exam I gave. I am very ...
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Why does heat flow from a region of higher temperature to one of lower temperature?

I have recently started thermodynamics and am unclear about reason behind the direction of heat flow, which is usually stated as a given fact. From the zeroth law of thermodynamics, originally, i ...
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Do Relativistic Gasses of Identical Particles Obey the Ideal Gas Law?

I am trying to determine the equation of state and see if $PV = nRT$ is satisfied. For an ultra-relativistic gas of identical particles in a volume $V$ the energy (I am assume there is no potential) ...
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Literature on Entanglement entropy

I am a Bachelor student and am about to start writing my Bachelor's thesis on theoretical physics. The topic revolves around entanglement entropy and I would like to know if there are any good books ...
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Can von Neumann entropy be used to characterize atomic and nuclear processes as spontaneous?

Gibbs free energy (involving entropy) can be used to characterize thermodynamic and chemical processes as spontaneous ($delta G < 0$). Can the same be done for atomic and nuclear processes by means ...
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Can a broken egg spontaneously reassemble itself (as in the video)?

According to the fluctuation theorem, the second law of thermodynamics is a statistical law. Violations at the micro scale, therefore, certainly have a non-zero probability. However, the application ...
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Entropy of Isothermal Expansion

I know that the change in entropy is 0 for reversible processes and is nonzero for irreversible ones. For isothermal free expansion (not reversible) the change in entropy is nonzero (i.e. proportional ...
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Why do we ignore higher-order derivatives of entropy with energy in deriving the Boltzmann distribution?

I am taking my first course in statistical mechanics, one point that I don't really get is the justification for ignoring higher-order derivatives of entropy w.r.t energy. We began the course by ...
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Problem with temperature using microcanonical in a small system

I have a system with two particles and three energy levels, with energy $\epsilon$, 2$\epsilon$ and 3$\epsilon$. The second level is degenerated. I want to find an expression like E(T) or T(E) where E ...
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Entropy change for fusion of ice do not tally from table values

In the data book, we have the following entropy values: $\mathbf\small{\rm{{S^\circleddash}[H_2O(s)]}}$ = 41 J/(mol K) $\mathbf\small{\rm{{S^\circleddash}[H_2O(l)]}}$ = 69.95 J/(mol K) Wikipedia ...
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Thermodynamic definition of an adiabatic process

I am posting about this because it seems to be a big issue and misconception in the thermodynamic literature. My issue is about adiabatic processes. As I see it there are two intrinsically different ...
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Thermodynamic equilibrium state of constant $(p,S)$ system

The internal energy as a function of its natural variables is: $$dU=-p dV+TdS$$ where $p$ is the system pressure and $dS$ includes only changes of the entropy due to heat transfer (the "...
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Do laptops become slow due to the second law of thermodynamics? Is it inevitable that classical or quantum computers will get slower over time? [closed]

The large scale composition of solid devices which comprise the hardware structure of modern computers are subject to the second law of thermodynamics as are all other physical objects. Assuming the ...
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Relationship between entropy and the number of symmetries

We count symmetries of a system by counting the number of transformations/operations under which a feature of the system remains unchanged. Entropy is a measure of the number of microstates that ...
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How is entropy increase in an isolated thermodynamic system consistent with the unitary invariance of Von Neumann entropy?

I was reading this StackExchange answer, which I will briefly summarize here. There is a room that is at a fixed temperature and is isolated from the environment. There is a block of ice inside the ...
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Closed formula for system's entropy

Suppose there exists a circle of radius $r$ and $n$ identical bouncing balls within this circle. Suppose this system has entropy $S$. Now reduce the radius to $r/2$ with the same number of bouncing ...
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Why doesn't a Coefficient Of Performance > 1 violate the second law of thermodynamics?

Apparently, if I understand correctly, one can move heat from a cold to a hot reservoir using less energy than the heat your are moving. This can be measured by the Coefficient Of Performance (COP). ...
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Problem regarding mean values of variations in statistical mechanics

Take a look at this previous question; in the answer by Julian Helfferich we arrive at the following formula for an infinitesimal change of entropy: $$dS = \frac{1}{T}\sum_i d(E_ip_i) - d(E_i)p_i$$ ...
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Why the volume of a cell in phase space should be equal to $(2\pi \hbar)^s$?

We want to properly define the concept of entropy using the Boltzmann's Definition of it. But there is a big problem: the coarse graining problem (Id est: How do we count the number of microstates in ...
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How to fully understand the Definition of Entropy?

In the context of Thermodynamics and Statistical Mechanics we encounter, basically, three different definition of entropy: First definition: Consider an isolated macroscopic system, it has a ...
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What if 1st law of motion and 2nd law of thermodynamics contradict?

Assume a large flat surface with a pile of books on it somewhere. Assume this system to be isolated and gravity to be present there. Also assume there to be a flow of time. As now you have ...
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Why don't we call this irreversible?

I've read that a quasi-static process in which entropy change only because of heat exchange: $\Delta S=\int \frac {\delta q} T$ is not called irreversible. The name irreversible is reserved for ...
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Change of Mutual Information in Isolated Quantum Systems

I was reading some publications regarding correlation and mutual information for composite quantum systems. I noticed that most papers give the expression for the mutual information to be: $$\Delta I(...
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Helmholtz Free energy: Examples of constant temperature and volume processes?

The concept of Helmholtz free energy has been giving me a lot of issues and I think the main reason for this is that I do not really have many concrete examples of physical phenomena that I can think ...
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The definition of Spontaneous in thermodynamics?

The definition of spontaneous is often briefly glossed over in most of the thermodynamics texts that I own. Peter Atkins in Physical chemistry defines spontaneous as follows Some things happen ...
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More reversible heat required to do the same work as an irreversible process?

Suppose we have the reversible isothermal process from state a to b as shown below: The work done by the system is simply equal to the area under the curve. The fact that this process is isothermal ...
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Why isn't the law of entropy applicable in the other direction of time? [duplicate]

If we have a system with the total energy concentrated in a few particles as the initial condition, law of entropy says that this energy will get more evenly distributed if the system is allowed to ...
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Does a broken symmetry lead to the second law of Thermodynamics? (Noether's Theorem)

So, Noether's Theorem states that for every conservation law, there is a corresponding symmetry. If that symmetry is broken, the conservation law no longer stands. Can this logic be applied to entropy?...
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Exact Heat Differential in Reversible Processes

From Clausius' theorem for a reversible process $C:$ $$\oint_C\frac{\delta Q_\text{rev}}{T}=0,\tag{1}$$ doesn't this imply that the differential $\delta Q_\text{rev}$ is exact? Or does $T$ serve the ...
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Can the number of microscopic configurations of a gas be expressed in terms of its temperature?

I'm new to the field of thermodynamics, but have been thinking about it recently, and wondered whether this statement has any truth in it. I doubt it is true, however I need to see whereabouts the ...
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Differential form of Massieu’s function [closed]

Massieu’s function is given by: $$F_{M}=-\frac{U}{T}+S$$ And its differential form is given by: $$dF_{M}=\frac{U}{T^{2}}dT+\frac{P}{T}dV$$ Well, it seems that: $$\frac{\partial S}{\partial T}=0$$ How ...
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Thermodynamics and the state postulate: should it be a Fourth Law?

The state postulate is as follows: The state of a simple compressible system is completely specified by two independent, intensive properties. My first question is whether there is any justification ...
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On including conserved charges when maximizing entropy of a statistical system

One approach towards constructing the probability of a state in a system is by maximizing the constrained entropy $$ S[p(n);\alpha,\beta] = -\sum_np(n)\log(p(n))\;+\; \alpha\big(\sum_nE_np(n) -\langle ...
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Interpretation of 2nd law of thermodynamics and observation in quantum mechanics

The fundamental lesson of quantum mechanics has been that an observation "disturbs" the system under analysis as exemplified in Schrodinger's cat thought experiment or wave-function collapse ...
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Does evaporation violate the second law?

Suppose I leave a glass of water on a table at STP. The water molecules at the surface of the water can be assumed to obey the Maxwell-Boltzmann distribution (at the least they obey a distribution of ...
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Why only heat energy is linked with entropy?

While calculating the change in entropy why do we only consider the change in heat energy? Is it because entropy means randomness and for randomness the more the average kinetic energy of particles ...
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Why is entanglement entropy in QFT infinite?

I have been reading some slides of Ed Witten about the Reeh-Schlieder theorem and entanglement in QFT (pdf). In it says that entanglement entropy in quantum field theory have a universal ultraviolet ...
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Can we really apply the second law to the entire universe?

I do not doubt the second law in general, just if it rigorously applied to the entire universe. Here's why I ask this 2nd law - restricted to isolated systems: "The second law may be formulated ...
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Shouldn't change in entropy always be 0?

We know that entropy is defined as $$dS=\frac{dQ}T$$ Now in any isolated system, by definition $dQ=0$. So should entropy change in any isolated process or system always be 0?
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Closed system in thermodynamics

If a closed system experiences a new work transfer while it undergoes a reversible process, does a net heat transfer from the system always occur? If not, please provide an example when a net heat ...
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Can two equally sized systems at different temperatures have different entropies? [closed]

Basically, it means that can a system have a higher "maximum entropic" state than another? Assuming both systems have equal number of molecules. All of molecules of both systems are ...
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What are entropic forces and how are they related to free energy minimization?

Are entropic forces only a result of "entropy maximization" (for isolated systems) and "free energy minimization"(for systems in equilibrium)? Can we think of phase transitions as ...
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Theoretical Otto and Brayton cycles are reversible and have efficiency less than the Carnot efficiency, so appear to violate 2nd law. Help

I understand Carnot's theorem, specifically the result that "the efficiency of all reversible engines operating between the same two temperatures is the same." The proof is by contradiction ...
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Problem deriving entropic uncertainty relation

In this paper the authors state that the inequality near the bottom of page 2 reduces to inequality (1) when $N=1$. However, I am struggling to get that result, as I have an extra minus sign in front ...
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What do we meant by “Thermally isolated universe”?

As we knew in general, $$dS=\frac{\delta Q_{rev}}{T}\geq \frac{\delta Q}{T}.$$ Consider a thermally isolated system so that the above inequality becomes $$dS\geq 0 \ \ \text{if} \ \ \ \delta Q=0. $$ ...
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When snow falls, temperature rises. Is this due to entropy?

A friend of mine told me that temperature rises when snow falls. And this is because condensation of water in snowflakes reduces entropy and the temperature of the air rises to compensate for this. Is ...
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Does diffusion do work?

Imagine I drop a sugar cube of 2 cubic centimeter into a cup of distilled water and then wait for the sugar molecule to break apart and dissolves into the soon to be solution. Is there any work done ...
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What interpretation can have a negative conditional entropy in quantum information? [closed]

So, I'm studying the basics in quantum information and many texts and papers have interpretations for entropy, relative entropy and conditional entropy, but none has an interpretation for a negative ...
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Separation of oil-water mixture and entropy

Imagine having the same volumes of olive oil and water in a bottle. When we shake the bottle long enough, we disperse the oil in the water and create an emulsion. However, if we wait, the oil will ...
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Why does entropy jump across a shockwave?

Using the Rankine-Hugoniot relations for a shockwave, one can show that entropy jumps across the shock, so that the entropy difference between upstream and downstream conditions is given by $$s_2 - ...

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