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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Entropy of a gas in a system and a gas mixture in another system

I could get concepts about entropy from the answer of the question below: What exactly is entropy? But I had some confusions in addition to that First Question:→ How would someone define random ...
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2nd Law of Thermodynamics - Reformulation Regarding Spontaenity of Processes

It is said that 2nd law predicts direction of spontaneous process. It does so by saying that direction of spontaneous process is that in which entropy of the isolated system increases or stays the ...
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Entanglement Hamiltonian of a subsystem and the reduced density matrix

I encounter a problem in finding the entanglement Hamiltonian of a subsystem. Suppose my system consists of two sites and two fermions, and the Hamiltonian of the full system is the following: \begin{...
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What's the name of this entropy based on particle density?

Say, at time $t$, the particle density in space is $\rho(\vec{x},t)$ and this distribution is normalized such that $\int d^3 \vec{x} \rho(\vec{x},t) = 1$. We can then associated a value similar to ...
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Why this perpetuum mobile won't work?

Design of this perpetuum mobile is based on brownian motion. When you place a small particle ($3\ \mathrm{\mu m}$) in liquid, you can see it moving randomly, because it gets hit by moving molecules. ...
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How does the Clausius statement imply the Kelvin statement of the 2nd law?

A common method to show the equivalence of the Clausius and Kelvin statements of the 2nd law is to show that breaking Kelvin implies breaking Clausius and vice versa. I understand the logic for ...
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A little question about entropy (Basic Thermodynamics)

Suppose I have connected a source temperature $T_{so}$ and a sink temperature : $T_{si}$. So I get work $W = Q(1-T_{si}/T_{so})$, where $Q$ is the heat energy transferred due to temperature difference....
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Steady state process/systems and entropy generation?

As far as I know in a steady-state process, each point in the control volume (system) does not undergo a change in state with time, which means that its properties don't change with time. However, How ...
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Is it possible to determine entropy change without thermal expansion?

I was recently told by a colleague that one could "easily calculate entropy change of a solid using only Cp and isothermal compressibility constant (along with experimental parameters:Vsolid, P0, ...
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Does gravity reverse entropy? [duplicate]

How I got interested:- A few days ago I was watching a few YouTube videos about reversing entropy and how it was impossible. But while thinking about it, it suddenly seemed like gravity reverses ...
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Entropy of the Universe and Quantum Information [closed]

From what I have understand, heat death of the universe requires a positive cosmological constant. And so when the universe achieves thermodynamic equilibrium, it shall have maximum entropy. Now I ...
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Practically speaking, why is a calculation of entropy change useful?

Entropy is a starting point for many advanced theoretical statistical mechanics books but beyond it just being negative or positive, what does it actually tell you? Specifically, what does the ...
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Role of carnot engine in the proof of Clausius' inequality

In the proof of Clausius inequality we take several carnot engines which take $Q_{oi}$ amount of heat from the heat reservoir at $T_o$ and dump $Q_i$ amount of heat to the $i^{th}$ process of the ...
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Understanding Clausius' inequality for irreversible process

Consider a system which is initially at a state $A$. Then it is moved to state $B$ absorbing $Q_h$ amount of heat from a heat reservoir at $T_h$. As the process is reversible so during heat exchange, ...
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Can total change in entropy be positive in a reversible process when there is non-PV work being done?

Change in gibbs free energy is said to be equal to the -(non-PV work done by the system) for a reversible change when the temperature and pressure are constant. $\Delta G=-w_{non PV,bysystem}$ However,...
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Not sure how to calculate entropy change in a quasi-static isobaric expansion

I'm working on a problem that states: Volume of $n$ moles of ideal monatomic gas increased from $V_0$ to $2V_0$ at constant $P_0$ in a quasi-static process. Calculate $\Delta W$, $\Delta Q$, $\Delta ...
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Heating a room with the window open

I am thinking about how the heating of a room changes from 0 to 20 degrees with and without the window open. If I heat it with the window closed, I have calculated the internal energy as follows: $$V ...
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Heat capacity at constant pressure

Is $C_p=T\left(\frac{\partial S}{\partial T}\right)_{P}$ true for both reversible and irreversible process? I know why is true for the reversible case but can't see if it might be true for the ...
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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 of ...
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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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