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36 votes

What would happen if I accelerated to 0.999c seconds before the heat death of the universe?

(1) Heat death is no switch that flips, it's a gradual process. You can't time it sharply. (2) There is no absolute time in special relativity, so it does make sense that it takes different times for ...
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27 votes
Accepted

Why is the second law of thermodynamics not symmetric with respect to time reversal?

The arrow of time in thermodynamics is statistical. Suppose you have a deterministic system that maps from states that can have character $X$ or character $Y$, to other states that can have character $...
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26 votes

What would happen if I accelerated to 0.999c seconds before the heat death of the universe?

There are a few tiny kinks on your logic, but we can soon straighten them out! In no particular order... You are implicitly assuming that the heat death occurs everywhere in the frame of the '...
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20 votes

Where does the irreversiblity came from if all the fundamental interaction are reversible?

There's a distinction between microscopic reversibility and macroscopic reversibility. Or if you will, a difference between something being irreversible in theory versus irreversible in practice. (Or ...
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14 votes

Local decrease of entropy, does it require life?

No life needed for this. All you need is for heat to flow away from the local region. It will carry entropy with it. Example: make yourself a cup of coffee. Put the cup on a table and wait while it ...
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13 votes

Entropy of the earth decreased since pre-biological times?

Entropy on the Earth has decreased over time as more and more structures and patterns have been added. The entropy of the earth has decreased over time due to the fact that it has cooled down ...
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  • 25.3k
13 votes

Entropy of the earth decreased since pre-biological times?

To differentiate itself from its surroundings, any living organism (no matter how simple) must decrease its entropy. Or, at least, it must ensure that its entropy increases more slowly than its ...
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13 votes
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How can Entropy be a state function (a property)?

I think the way you write the two conditions may be misleading. $$ \begin{align} {\Delta S}_{rev} &= \int_1^2 \delta Q / T \\ {\Delta S}_{irrev} &= \int_1^2 \delta Q / T + S_{gen}. \end{align} ...
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12 votes

Where does the irreversiblity came from if all the fundamental interaction are reversible?

Irreversibility comes from the thermodynamics: the probability that we return to the same state in any reasonable amount of time is extremely small. In more technical terms: the entropy is increasing. ...
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  • 38.8k
11 votes

Why is the second law of thermodynamics not symmetric with respect to time reversal?

A long comment. Thermodynamics can be shown mathematically to be an emergent theory from statistical mechanics. Its laws are observational laws, deduced from variables and their measurements, that are ...
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  • 222k
11 votes

How is Newton's first law compatible with transport equations?

In order to have a (constant, non-zero) flux you need either no force at all or else a balance of forces. The situations ordinarily under discussion here are where there is either friction or a ...
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8 votes

Is there a quantum of entropy - and how large is it?

In physics, we normally define entropy as $S = k \ln \Omega$, where $k$ is Boltzmann's constant and $\Omega$ is the number of microstates consistent with the observations you've made of the system. ...
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  • 34.3k
7 votes

Where does the irreversiblity came from if all the fundamental interaction are reversible?

This question is asking why, if at the quantum realm of particles, processes can happen in reverse (particle interactions obey time reversal transformations), why does macroscopic matter (which is ...
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  • 25.3k
7 votes

Why is the second law of thermodynamics not symmetric with respect to time reversal?

Yes there absolutely is a well-known apparent (classical) contradiction here. Classical mechanics is symmetric under $t \to - t$, i.e. for any given motion the reverse motion is also possible. As you ...
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7 votes

Why is work entropy-free?

Entropy is generated in work processes involving viscous dissipation of mechanical energy such as rapid expansion or compression, stirring, etc.
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  • 27.9k
7 votes
Accepted

Entropy of the earth decreased since pre-biological times?

An organism (or any self-replicating arrangement of matter) is a machine that concentrates environmental negentropy in itself while increasing total system entropy. The false belief that evolution ...
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7 votes

Are Humans and DNA the only things capable of creating order (Negentropy)?

Any heat engine, generator or a living organism is performing useful work, thus reducing entropy somewhere (i.e., increasing order somewhere), although simultaneously increasing the overall entropy of ...
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  • 38.8k
6 votes

Heat engine efficiency curse

The difference between your two processes is that the left hand column is a reversible process - or, at least, it can be made reversible as long as we use the falling brick to do work without letting ...
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6 votes

Why does the "entanglement entropy" provide a necessary and sufficient condition for bipartite entanglement?

Consider a bipartite system and let $\rho$ denote a pure state density operator with reduced density matrices $\rho_1$ and $\rho_2$. OP proved that if $\rho$ is a product state, then $S_{\mathrm E} (\...
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6 votes

Why is the second law of thermodynamics not symmetric with respect to time reversal?

The laws of physics are differential equations, and to solve a differential equation you need two things: the equation itself tells you how the value of some physical variable at each point of a ...
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6 votes

Why is entropy an extensive property?

There is some ambiguity in how entropy is defined in thermodynamics/stat. physics, as, e.g., discussed in this answer. To take the two most common definitions: In thermodynamics entropy is defined ...
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  • 38.8k
6 votes

How can Entropy be a state function (a property)?

Your error is in assuming that $\int_1^2 \frac{\delta Q}{T}$ is the same for the two processes. As an example, consider an ideal gas whose initial state is given by $(V_0,T_0)$ and whose final state ...
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  • 51.8k
6 votes

Ensembles in statistical mechanics

An Ensemble is a group of systems that are microscopically different but macroscopically the same. For example, for an isolated box containing 1 mol of gas, which means we have around $6\times10^{23}$ ...
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  • 780
6 votes
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Replacing variables after Legendre transformation

Note that $$T(S,N,V) = \frac{\partial U}{\partial S} (S,N,V) $$ and that under certain conditions on these functions we can invert this relation to find $S(T,N,V)$. We then define $$F(T,N,V) = U(S(T,N,...
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5 votes
Accepted

How can it be shown that a system's entropy is reduced by cooling it?

You're looking at it the wrong way. If your equation was $$S=\frac{some constant}{T}$$ I would agree that it says the entropy increases when T decreases. But we definitely don't have something of that ...
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5 votes
Accepted

Is time still (frozen) for a single isolated particle?

You can certainly imagine such a Universe with one lonely structureless and cold particle, interacting with nothing and living in some eternal and unchanging spacetime. Of course such a Universe it is ...
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  • 34.3k
5 votes

Where does the irreversiblity came from if all the fundamental interaction are reversible?

then where does the irreversibility come from? You mean macroscopic irreversibility, our inability to set up or observe a macroscopic process that retraces past states of a known spontaneously ...
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5 votes

Local decrease of entropy, does it require life?

It happens about 50 times in a second in any internal combustion engine, including cars. Without life. Life has no specific meaning in thermodynamical sense.
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5 votes

Why is work entropy-free?

Because the entropy in this notes is defined in terms of the heat transfer: $$ dS=\left(\frac{\delta Q}{T}\right)_{int, rev}, $$ which is the increase of the internal energy not associated with work. ...
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  • 38.8k
5 votes

Reversibility of the arrow of time

It is a convention that we take the direction of increasing time as the direction of increasing entropy. We could reverse the convention. But in either case the thermodynamic arrow of time must align ...
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