# Tagged Questions

A 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 when mixing water at different temperature

Suppose two amounts of water of the same mass, but with different temperature, are mixed. Then the entropy of the hot water decreases, but the entropy of the cold water increases due to heat transfer. ...
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### Entropy Change for a Thermally Isolated System

Clausius' Theorem states that $\int\frac{dQ}{T}\leq0$ for a closed cycle, with equality for a reversible cycle. Suppose we wish to take our system around a closed cycle such that the path from A to B ...
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### Where is the flaw in this machine that decreases the entropy of a closed system?

I was thinking about a completely unrelated problem (Quantum Field Theory Peskin & Schroeder kind of unrelated!) when the diagram below sprang into my mind for no apparent reason. After some ...
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### Why do many people link entropy to chaos?

I understand that, in thermodynamics, entropy has a precise definition (the infinitesimal change of entropy being the infinitesimal heat transfer divided by the temperature), and that in statistical ...
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### How to derive entropy from density of states?

I'm trying to derive the entropy of a black hole, given the density of states of a bosonic string (the details are not relevant). The density of states is $$\omega(E) = E^\alpha e^{\beta E}$$ The ...
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### How is a irreversible process (conventionally) represented on a $T-S$ plane and why cannot it be (really) represented?

A reversible process can be represented on a $T-S$ plane, and the area under the curve is the heat exchanged by the system. On $P-V$ plane a irreversible process is conventionally represented with a ...
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### Why don't photons split up into multiple lower energy versions of themselves?

A photon could spontaneously split up into two or more versions of itself and all the conservation laws I'm aware of would not be violated by this process. (I think.) I've given this some thought, and ...
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### Relation between entropy and internal energy

I am confused as to what is the relation between entropy and internal energy. Entropy is always presented as a measure of the randomness in a system. So when we supply heat to a well insulated system ...
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### Does measurement, quantum in particular, always increase the total entropy?

Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this ...
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### Is Bekenstein entropy limit inconsistent with universal continuity?

It is unknown whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Can universal continuity be experimentally falsified? Is the universe finite ...
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### Books on entropy [closed]

What books introduce entropy in a intuitive, elementary way (at most, for a person with undergraduate physics studies)? The book should not necessarily introduce entropy in relation only to ...
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### Accessibility by reversible processes and the Second Law of Thermodynamics

One common way of motivating the existence of Entropy as a state function is the following. Let us take the Clausius/Kelvin-Planck statement of the second law, from which we can deduce Clausius' ...
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### Change in entropy of thermodynamic environment during isobaric or isochoric processes

When an ideal gas follows a isobaric or isochoric transformation (no matter if it is reversible or not) I'm not sure what is the change in entropy of the thermodynamic environment. First of all, ...
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### How did steady-state universe deal with entropy?

Until the 1960's the general consensus was that the universe is infinite years old (steady-state). The second law of thermodynamics says that entropy always increases, so we'd expect that within a ...
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### Reference request for low entropy big bang

There is a somewhat widely accepted argument that the second law of thermodynamics exists because the universe began in a low-entropy state. I'm writing a paper that mentions this (and must be ...
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### Why would a Boltzmann brain be transient?

The Boltzmann brain idea as I understand it: suppose the universe has an infinite lifetime. Once heat death is achieved, there are no more large-scale structures to the universe -- everything is just ...
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### Entropy and Clausius inequality

From the Clausius inequality we can derive that the efficiency of a Carnot (reversible) cycle is given by: $$e= 1 - \frac{T_c}{T_h}$$ Is this true for every reversible cycle? Is the efficiency of all ...
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### Does conservation of information mean that the direction of causality is arbitrary? [duplicate]

If it is the case that the information content of the universe is conserved, and the past can be constructed from a complete knowledge of the future just as easily as vice versa, then is there any ...
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### Can black holes grow via accretion of dark matter particles?

I'm assuming that the answer to the question in the title is a resounding yes. Since Baryonic matter and dark matter interact via gravitational forces. If this is the case how is information not lost ...
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### If a flywheel is spinning at say 1,000 rpm, would an input of 500 rpm would actually slow it down? [closed]

When a flywheel is stationery, an input of 500 rpm would translate to less than 500 rpm in the flywheel considering entropy, but what happens if the flywheel is already running at 1000 rpm, wouldn't ...
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### Home Work Help: Calculating Entropy for Melting Ice - Clarification on answer

The question states: What is the change in entropy for the process to completely melt 8.0 kg of ice at 0°C? The formulas for Entropy we've been introduced to are: ...