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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Alternative interpretation of the second law of thermo [closed]
I have had this thought for a while and I was wondering whether it's valid.
Entropy is often described as the amount of "useable" energy in a system
at a micro level, entropy is related to ...
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Why is the holographic encoding from Bekenstein-Hawking entropy remarkable?
The holographic encoding interpretation from the Bekenstein-Hawking entropy is due to it scaling with the area $S_{BH} = A/4$ of the surface, rather than the volume $V$. While I am aware that most ...
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Can increase in entropy increases the probability of finding something specific [closed]
See if we take a bookshelf with 10 books in it and drop all of them in a room and repeat this process infinite times. So we can say that entropy of room increases and now we have to find a specific ...
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Is the concept of entropy a result of limited technology?
I know that entropy is the energy within a system that is unable to do useful work. However, there was a time in which we were unable to harness the energy of the wind or the sun, and now we can, ...
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Are von Neumann entropies of complementary but physically distinct subsystems in time-dependent settings identical?
We assume a quantum system AB with subsystems A and B and take the Schmidt decomposition of a state $\vert\psi_{AB}\rangle=\sum_i\lambda_i \vert a_i\rangle\vert b_i\rangle$ defined on the compsite ...
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Free energy change in reversible/irreversible processes
Yet another follow up to this question,
I am struggling to understand the example provided in Chet Miller's answer:
An example of this is expansion of an ideal gas in contact with an ideal constant ...
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Difference between Reversible and Irreversible processes in Physics vs. Chemistry
In Physics a reversible process is defined as one in which the system can be returned to its initial conditions via the same path (along the PV Diagram), and every point along the path is an ...
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Why do we put factors of zero in a Lagrangian that is to be extremized?
According to the Wikipedia page on Lagrange multipliers under the section - Example 3: Entropy, it is written that:
$$f(p_1,p_2,\ldots,p_n) = -\sum_{j=1}^n p_j\log_2 p_j$$
For this to be a ...
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How the temperature used in second law of thermodynamics and ideal gas law equivalent? [closed]
I was reading Theory and Problems of Thermodynamics by Schaum's Outline series and there the author starts from some axioms (which are the thermodynamic laws, excluding the zeroth and third). Then he ...
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Second law of thermodynamics and Unitarity of quantum mechanics [duplicate]
From the second law of thermodynamics, we know the entropy must be increasing in an isolated system, such as our Universe. On the other hand, we have quantum mechanics which, I think, somehow tells us ...
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How a thermodynamical system relaxes to equilibrium?
For a system in contact with a reservoir with well-defined constant temperature $T$, its change in Helmholtz energy satisfies the following inequality:
$$\Delta F \le -W_{by}$$
where $W_{by}$ denotes ...
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Equivalence of mixed states
I have questions regarding equivalence of mixed states. Consider a single photon and its polarization as an example. If I know that some kind of process creates a single photon in an exact ...
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Questions on $\Delta S = \frac{q}{T}$
My Thermodynamics book discusses three types of expansions of an ideal gas and the change in entropy $\Delta S$ associated with each expansion, all of which take an ideal gas in a piston from $V$ to $...
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Can someone explain this to me? About reversible computing with finite energy and thermal equilibrium
In Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, they examine the implications of dark energy on the ultimate fate of life.
Then they say this,
It was long thought ...
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Reconciling the notions of $\Delta G$ as a criterion of spontaniety and as the maximum non-expansion work
For a closed system that stays at constant temperature and pressure, regulated by the envrionment acting as a reservoir, it can be proven that
$$\Delta S^\text{Univ} \geq 0 \iff 0 \geq \Delta G,$$
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$dq_{rev}$ and $dq$, which one is larger? [closed]
Im learning about entropy and some concepts makes me confusing.
For a reversible and irreversible process with a same initial state and final state, it is said that entropy change of a system is ...
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What is temperature in the classical entropy definition?
Entropy change for a system is defined classically as:
$$dS=\frac{\delta Q_{rev}}{T}$$
where $\delta Q_{rev}$ is infinitesimal reversible heat that flows in a system.
I don't understand whether $T$ ...
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Proof of $dE = T dS − P dV + µdN$
I'm following this book. The author states The First Law of Thermodynamics as follows:
$$dE = đQ + đW + đC$$ , (3.50)
where
– đQ = energy put into the system thermally by an environment, such
as a ...
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Clausius' Theorem Difficulty
I've found these notes on foundations of Thermodynamics/Statistical Mechanics to be quite helpful. However, I have come across a concept on page 17 that I can't quite seem to wrap my head around. The ...
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Helmholtz free energy from internal energy formula
I have just encountered this formula for obtaining the Helmholtz free energy $F(T,V)$ of a system from the internal energy $U(T,V)$:
$$F(T,V)=U(0,V)-T\int_0^TdT'\dfrac{U(T',V)-U(0,V)}{T'^2}.$$
The ...
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Correlation between mutual information and thermodynamic entropy
Does a system having a lower thermodynamic entropy imply that there is greater mutual information between the variables associated with its constituent parts? I.e., in a lower entropy system, any one ...
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Confusion About Entropy
I have a lot of confusion around the concept of Entropy.
If we know a system's entire microstate, the number of ways it can exist in that microstate is 1. So, if we fully define our system, it will ...
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Reversible thermodynamics processes
A problem asks me to find the entropy increment in the machine operating some thermodynamic cycle. Can I assume that any closed cycle can (theoretically) be obtained by using two reservoirs at some ...
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Heat from a cold reservoir to a hotter system, which is converting it to work? [closed]
Recently I had encountered this question, "Derive an expression for the maximum work done by $1$ mole of a monoatomic ideal gas, initially contained in a cylinder of volume $V_0$ at a temperature ...
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Why don't superconductors, which have zero electrical resistance, violate the second law of thermodynamics?
There are bunch of questions on here asking whether superconductors really have exactly zero resistance and answers saying they do. My question is how this doesn't violate the second law of ...
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Entropy Departure - BWRS Equation of State [closed]
Edit: This was not a homework problem. I simply pulled an example from a textbook to easily illustrate and convey the problem at hand.
I am seeking some assistance in evaluating the entropy change of ...
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Functional derivative and entropy
I just started to read about (entanglement) entropy for CFTs. I have a confusion that probably originates from a misunderstanding about functional derivatives.
For instance, in (4.21) in this review ...
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Arrow of time as the result of a feedback loop that stabilizes an inheret unstable reversible time [closed]
I am searching to find some literature on idea i am having, regarding the "arrow of time".
The main idea is an expansion of the main theme of an Asimov sci-fi novel, where he postulates ...
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Can we think of entropy and time as the same thing? [duplicate]
My assumption is that entropy is a change in the distribution of energy in one direction. The universe is a system going from low to high entropy. Can time be described without the change of entropy? ...
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Matrix Factorization into a Real Times a Unitary
I am working on my Final Degree Project involving entanglement entropy, for which I am reading H. Cassini and M. Huerta's paper Entanglement entropy in free quantum field theory
(J.Phys.A42:504007,...
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A reversible transformation, but there is finite temperature heat transfer?
Suppose to have 3 heat reservoirs, the first at temperature $T_1$, the second at temperature $T_1+dT$ and the third at temperature $T_2>T_1$
Then, consider a system, which volume is constant, in ...
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Is entropy of a system, strongly coupled with another one, well defined?
Consider two, strongly coupled systems, $A$, and $B$, and suppose to be interested to the entropy of $A$.
The Boltzmann definition of entropy, for A, is $S_A=k_B \ln (\Omega_A)$, where $\Omega_A$ is ...
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Has the entropy of a single photon ever been measured?
Light fields have entropy, as already discussed by Planck.
As a consequence, photons have entropy.
The entropy of single photons is some factor of order unity times the Boltzmann constant. The topic ...
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An entropy-like measure for a pure state? [closed]
It came to my mind that can we describe the flatness of a pure quantum state $\psi$ in terms of an entropy-like measure? Obviously, a Dirac delta -like distribution $|\psi|^2$ has a low "entropy&...
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Why black hole erase information
It is usually said that according to the no hair theorem, black holes erase the information enter them which reduce the entropy and imply the so called "information paradox".
The problem is ...
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How does Bolztmann Brain explain experience of time? [closed]
If a Boltzmann Brain existence is fleeting due to the absence of supporting organs and environment, how does the thought experiment account for the passage of time it experience in its brief existence?...
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Entropy change for a real gas via Peng-Robinsons EOS
Consider a process with inlet conditions ~300K,~50Bar and outlet conditions ~350K,~150Bar. Entropy departures as per Peng-Robinsons EOS. I am evaluating the entropy change via the following:
∆𝐒 = 𝑺𝒅...
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Maximum Entropy Principle with inequality constraints
It is well known that, maximizing the entropy of the joint distribution $P(x_1,...,x_n)$ of a random vector $(X_1,...,X_n)$ subject to equality constraints for the mean vector ($\mu$) and the variance ...
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Is the value $k \ln 2$ the largest or the smallest entropy that a single particle can carry? [closed]
Sorry, but I lost the reference of the author telling this.
Is $k \ln 2$ the largest or the smallest entropy that a single particle can carry?
And why is this so?
EDIT:
It was a paper from the 1970s.
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In the context of the holographic principle, is the bulk-boundary correspondence due to entanglement?
According to the holographic principle, a "bulk" region of D dimensions corresponds to a "boundary" region of D-1 dimensions. In this context, the laws of physics of the bulk can ...
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Entropy balance of surroundings in open systems
In my text book, "Chemical, Biochemical, and Engineering Thermodynamics" by Sandler.
The entropy balance equation for an open system is defined as,
$$\frac{dS}{dt}_{sys} = \sum_k M_kS_k + \...
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Why is all matter in the universe, not found at its lowest state of potential energy?
Preface: it may be of interest that I am a second year Biology student, with no experience in studying Physics and a very basic understanding of Mathematics. ...
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Does the Sun increase entropy?
The Sun generates heat via fusion. The heat from this reaction gets distributed around the solar system and beyond. This process of spewing heat and radiation all over the place doesn't immediately ...
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Is entropy in the third law of thermodynamics a continuous quantity?
In the third law of thermodynamics, entropy goes to zero or to a constant value at vanishing absolute temperature. The change of entropy also goes to zero.
The third law is valid in the thermodynamic ...
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What is the average increase in entropy per unit space?
The second law suggests that averaged over a large enough space and time, entropy always increases.
The rate of increase obviously depends on local conditions. The increase in Entropy in a year in ...
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How to calculate the total entropy of dS black holes?
In several articles where the thermodynamics of dS black holes have been investigated, the entropy part of the model or the total entropy has been analyzed based on the entropy of the black hole ...
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Is there entropic force in a black hole?
A black hole is regarded as a thermodynamic system that has entropy. Its horizon has a temperature and corresponds to a macroscopic system, thus occupying a large number of states. In this perspective,...
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Reverse entropy? [closed]
I don't know much about entropy but all I know is the energy of a system tends to spread, more generally things tend to chaos. And entropy is not reversible, you can not stick a broken egg together.
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How can I derive the second law of thermodynamics from Newton's second law of motion? [duplicate]
Do you know of an elementary proof for the second law of thermodynamics, for example, from the Newton laws or perhaps some particular model in which it is equivalent/reduces to it?
My naive concept of ...
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Why is zero entropy possible for a solid at absolute zero temperature?
The third law of thermodynamics states that the entropy of a perfect homogeneous solid is zero at absolute zero temperature.
The reason to ask for "perfect and homogeneous" is that such a ...
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