A important property of all systems in thermodynamics and statistical mechanics. Entropy characterizes the degree to which the energy of the system is *not* available to do useful work

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Connection between entropy and energy

An isolated system $A$ has entropy $S_a>0$. Next, the isolation of $A$ is temporarily violated, and it has entropy reduced $$S_b ~=~ S_a - S,\space\space\space S\leq S_a.$$ Is it true to say: the ...
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System moves away from equilibrium $\rightarrow$ it has energy added?

Suppose there is an isolated system $A$ at time $(-\infty, t_1)$, whose entropy is $S=S_{max}$, i.e. it is at thermodynamical equilibrium. Between moments $[t_1, t_2)$ the isolation is violated and ...
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Reference paper to support information — energy relation ($kT \ln2 \rm\frac{J}{bit}$)

In answer to Maxwell's Demon Constant (Information-Energy equivalence) there is stated that one bit of information allows to perform $kT \cdot \ln2$ Joules of work. Which paper supports the ...
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Is a closed system receiving heat guaranteed to have entropy below maximum?

Isolated system will preserve its entropy unchanged (for fully reversible system) or it will increase its entropy (for system with irreversible processes). For a closed system, it can receive energy ...
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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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Does the second law of thermodynamics tell me how the entropy changes?

In thermodynamics I can e.g. compute the properties of ideal gases with certain energies $U_1,U_2$ in boxes with certain volumes $V_1$ and $V_2$. Say I have two such boxes and they have some specific ...
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Did really everything begin with a state with very low entropy?

As emphasized by Penrose many years ago, cosmology can only make sense if the world started in a state of exceptionally low entropy. The low entropy starting point is the ultimate reason that the ...
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What's the validity of the thermodynamic definition of entropy?

Thermodynamic Entropy Variation is defined as $$\Delta S = \int_i^f \frac{dQ}{T},$$ where $i$ and $f$ are the initial and final states of the process. My question is: does this equation apply to ...
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What is a qualitative explanation for order of values of standard entropies of formation for isomers of hexane?

I have literature values for the standard enthalpy and Gibbs energy changes of formation at 298 K, $\Delta H_\text{f}^o$ and $\Delta G_\text{f}^o$, for product in the ideal gas state. Since $G=H-TS$ ...
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Is there an abstract notion of heat within a microscopical system?

The microstates of a system are said to be unobservable. I can introduce the entropy as a measure of the number of microstates, which lead to the same macroscopic variables. So in this detailed ...
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Statistical interpretation of Entropy

I'm preparing my statistical physics course, and while writing the lecture notes it says that a system with non distinguishable particles has much less microstates asociated with a particular ...
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Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy The speed of light c converts between space and time and also appears in e=mc^2. Maxwell's Demon can turn information supplied ...
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Are information conservation and energy conservation related?

as evident from the title, are both, conservation of energy and conservation of information two sides of the same coin?? Is there something more to the hypothesis of hawking's radiation other than ...
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Entropy change in a cycle with two isochoric and two adiabatic processes [closed]

Prove that the change of Entropy in a cycle with two isochoric and two adiabatic processes is 0. How can I prove that? Thanks!
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What meaning do changes in the absolute value of Gibbs free energy have in a simple expansion process?

Below is a simple representation of the thermodynamics of a steam turbine. Stream kinetic and potential energy changes are neglected and no other type of non-PV work is done besides shaft work. ...
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How long will my fridge magnet stay attached to my fridge?

I have a 500 gram neodymium magnet. It is stuck to my fridge. With the constant pull of gravity trying to pull it off how long would it stay attached to fridge? For arguments sake lets say my fridge ...
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Joining the definitions of entropy

$\int \frac{Q_{rev}}{T} = \Delta(k_B\ln\Omega)=\Delta S$ Could anyone give some definite proof for this? I was able to prove that the two definitions of change in entropy are equivalent for an ...
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Deriving an Expression for Entropy

How to derive an expression for entropy in form of $S = \ln \Omega$ from the form $\displaystyle{S = - \sum_i \; p_i \ln p_i}$ ? That is the last formula taken as a definition of entropy. Just a ...
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Maxwell's Demon bug, trapdoor space and time

What about the size of the door (space) and how long has it to be opened (time)? I think Maxwell's demon would have a problem with space, if the door is too wide (more than one particle size), then ...
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How to choose the right units to compute the phase space volume in classical statistical mechanics?

Without the natural unit $\hbar$, why doesn't it seem to be a problem for Statistical Physics to define $$S=k_B\ log(\Omega)\ ?$$ If $\Omega$ is given in one unit system and I switch to other units ...
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Nonextensive statistical mechanics

I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times ...
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How is thermodynamic entropy defined? What is its relationship to information entropy?

I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states. How is ...
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Simple question about a gas in a box with a moving wall

David Albert is a philosopher of Science at Columbia. His book "Time and Chance" includes this example (p 36). A gas is confined on one side of a box with a removable wall. "Draw the wall out, ...
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Restrictions on defining microstates (Entropy)

If we have an isolated system $Sb$ with thermodynamic entropy $Eb=X$ (and growing by the 2nd law of thermodynamics), we could define an abstract system $Sa$ (containing the system $Sb$) but define ...
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Explaining Arrow of Time with Entropy

WARNING: Possibly a naive post. Hi guys. I just watched on BBC, [some show] yesterday (sunday) where the host talked about Arrow of Time, where by 2nd law of thermodynamics states that "nature" is ...
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Best example of energy-entropy competition? [closed]

What are the best examples in practical life of an energy-entropy competition which favors entropy over energy? My initial thought is a clogged drain -- too unlikely for the hair/spaghetti to align ...
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How does lifting an object effect its entropy

I have figured out that: When photons leak out from a container, the entropy of the photon collection increases, because each photon has a different escape time. Photons that have leaked out from a ...
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Do all closed systems, only considering kinematic/mechanical principles, exhibit time reversal symmetry?

It makes a lot of sense to me to imagine a cannonball flying through space as not so much experiencing a macroscopic non-conservative drag force, but as pushing a bunch of air molecules and giving ...
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Energy of unmixing

Mixing of two different fluids is associated with an increase of entropy. Conversely, separation of two gases must be associated with a decrease of the entropy of the two fluids. Is there a minimum ...
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Why was the universe in a extraordinarily low-entropy state right after the big bang?

Let me start by saying that I have no scientific background whatsoever. I am very interested in science though and I'm currently enjoying Brian Greene's The Fabric of the Cosmos. I'm at chapter 7 and ...
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How to understand temperatures of different degrees of freedom?

So I'm reading this book, where after the preface and before the models there is a section called General Notions and Essential Quantities, which introduce some things I don't understand. They regard ...
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339 views

Defining Orderly/Chaotic states in terms of entropy?

I'm trying to properly understand the meaning of entropy, and how the universe is moving from an orderly state to a chaotic one. If a glass of wine (for example) only has meaning to a human, what ...
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What is the current science on entropic gravity?

In the past couple of years there has been some buzz about 'entropic gravity', including here on stackexchange in Jan 2011. Many say that there is no way that gravity can be entropic, while others ...
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Second law of thermodynamics and a bunch of magnets

Say I put a bunch of powerful square magnets on a nearly frictionless table in a disordered fashion. The second law of thermodynamics states that the system shall spontaneously get more disordered, ...
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Is this a known entropy formula?

While playing around with a variant of the one-dimensional Ising model with periodic boundary conditions I came up with a formula, let's call it $F$, whose form looks suspiciously like an entropy ...
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Use of escort distribution in nonextensive stat. mech

In some of the articles which I read recently, I happen to see the following statement. In Nonextensive statistical physics, it is inappropriate to use the original distribution $P=(p_i)$ ...
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Can a single classical particle have any entropy?

recently I have had some exchanges with @Marek regarding entropy of a single classical particle. I always believed that to define entropy one must have some distribution. In Quantum theory, a single ...
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The entropic cost of tying knots in polymers

Imagine I take a polymer like polyethylene, of length $L$ with some number of Kuhn lengths $N$, and I tie into into a trefoil knot. What is the difference in entropy between this knotted polymer and ...
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Entropy of an empty universe

After watching the first episode of wonders of the solar system, one question came up which is not explained. Bryan Cox says that ultimately the universe will be devoid of matter, so not even a ...
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How bright can we make a sun jar?

A sun jar is an object that stores solar energy in a battery and then releases it during dark hours through a led. Assume: a $65cm^2$ solar panel a 12h/12h light/dark cycle insolation of ...
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Why it is said that Universe is an isolated system?

I have read in many places "Entropy of an isolated systems never decreases" And as a corollary: "As Universe is an isolated system(I) then its entropy is constantly increasing(II)" I) ...
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Relation between classical and quantum information

It is known that for a classical system the amount of information needed to store its state is the same as the amount of information that can be stored in that system. This amount is equal to ...
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If 100% of the energy from the sun is reflected back into space

100% of the energy from the sun is reflected back into space, it's just shifted from a low-entropy state to a high-entropy state, and from a high frequency (ultraviolet) to a low frequency (infrared). ...
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Can the entropy of a subsystem exceed the maximum entropy of the system in quantum mechanics?

Quantum mechanics has a peculiar feature, entanglement entropy, allowing the total entropy of a system to be less than the sum of the entropies of the individual subsystems comprising it. Can the ...
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Why is there an absolute entropy?

Why is there an absolute entropy? Given any non-discrete probability distribution, we don't really have an absolute entropy because the entropy depends on the parametrization of the distribution ...
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Is there a four-dimensional definition of entropy?

It seems odd that entropy is usually only defined for a system in a single 'slice' of time or spacelike region. Can one define the entropy of a system defined by a 4d region of spacetime, in such a ...
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The full entropy quote

What is the full text (and possibly the source) of the summary of the 3 laws of thermodynamics that goes something along the lines of "Can't break even, can't win and can't even stop playing the ...
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How to vizualize a heat pump microscopically?

Hey guys, while learning thermodynamics i wondered how a the principle of a heat pump would look at a microscopic level, not on a quantum mechanical level. I learned that when a hot and a less hot ...
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Experiments that measure the time a gas takes to reach equilibrium

If you take two ideal gases at different temperatures, and allow them to share energy through heat, they'll eventually reach a thermodynamic equilibrium state that has higher entropy than the ...