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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The entropy of a static granular mixture

Regarding static granular mixtures (pile of sand - particles with different sizes), is there an expression that will give me the entropy of such a mixture? I am interested in finding the entropy of ...
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Confusion regarding entropy, reference papers request

1.a In paragraph at Wikipedia/Entropy it is stated: This is because energy supplied at a high temperature (i.e. with low entropy) tends to be more useful than the same amount of energy ...
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Relation between external magnetic field intensity H, magnetisation M and the entropy?

How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in ...
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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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How did the energy/entropy/volume/pressure/temperature relationship exist at the Big Bang and how did it evolve thereafter?

According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big ...
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What is the physical or mathematical meaning of the Gibbs-Duhem equation?

The Gibbs-Duhem equation states $$0~=~SdT-VdP+\sum(N_i d\mu_i),$$ where $\mu$ is the chemical potential. Does it have any mathematical (about intensive parameters) or physical meaning?
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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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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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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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What physical processes may underly the collisional term in the Boltzmann equation, and how do they increase entropy?

Consider particles interacting only by long-range (inverse square law) forces, either attractive or repulsive. I am comfortable with the idea that their behavior may be described by the collsionless ...
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How is information related to energy in physics?

I recently attended a talk by Dr. Ravi Gomatam on 'quantum reality', where the speaker suggested, that conservation of energy is not a fundamental law, and is conditional, but the conservation of ...
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Ignorance in statistical mechanics

Consider this penny on my desc. It is a particular piece of metal, well described by statistical mechanics, which assigns to it a state, namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
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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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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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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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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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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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Second law of Thermodynamics: Why is it only “almost” always true that entropy is non-decreasing? [duplicate]

Wikipedia - Second law of thermodynamics: ...the entropy of any closed system not in thermal equilibrium almost always increases. I understand that the second law of thermodynamics is based on ...
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What does third law of thermodynamics tell us?

I just have a question concerning the third law of thermodynamics. The third law describes that the entropy should be a well defined constant if the system reaches the ground state which depends ...
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Is a world with constant/decreasing entropy theoretically impossible?

I'm not 110% sure exactly what I mean by this question. It was sparked by a friend who said he wished the law of entropy were reversed, so he wouldn't have to worry about cleaning the bathroom. ...
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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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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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Why does maximal entropy imply equilibrium?

From a purely thermodynamical point of view, why does that entropy have to be a maximum at equilibrium? Say there is equilibrium, i.e. no net heat flow, why can the entropy not be sitting at a ...
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Energy formula for separating $O_2$ from mixture of $O_2$, $NH_3$ and $H_2O$

I have a physics problem I'd like to make sure I get correct. The practical aspect of this problem is that the photosynthetic efficiency of algae is inhibited with dissolved O2 in the growth medium, ...
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Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? I have never seen dissipation explained, although what I have seen a lot is descriptions of ...
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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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212 views

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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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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Entropy of a mass arrangement around the earth

An mind experiment, taking the entire Earth as an isolated system Then this is the initial state: N masses are distributed around the earth, at different height. (for example we can use a single ...
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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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Can heat be extracted and concentrated? [closed]

If one could devise an answer to this question, electricity would be free for everyones disposal. (seems like a good dream but in reality free energy will be this worlds downfall)
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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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Renyi entropy in physical systems

We know that the Shannon entropy $H(P)=- k_{\mathrm{B}}\sum_i p_i \ln p_i$ is mostly the entropy of the thermodynamic systems. Does the Renyi measure $H_{\alpha}(P)=\frac{1}{1-\alpha}\log \sum ...
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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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Renyi fractal dimension $D_q$ for non-trivial $q$

For a probability distribution $P$, Renyi fractal dimension is defined as $$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ ...
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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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Geometric entropy vs entanglement entropy (dependent on curvature coupling parameter)

I have a quick question. In hep-th/9506066, Larsen and Wilczek calculated the geometric entropy (which I believe is just another name for entanglement entropy) for a non-minimally coupled scalar field ...
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How are possible microstates discerned in Gibb's entropy formula?

On the entry of Gibb's entropy formula on Wikipedia, the following definition is given: "The macroscopic state of the system is defined by a distribution on the microstates that are accessible to a ...
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Motivation for maximum Renyi/Tsallis entropy

The Conditional limit theorem of Van Campenhout and Cover gives a physical reason for maximizing (Shannon) entropy. Nowadays, in statistical mechanics, people talk about maximum Renyi/Tsallis entropy ...
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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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Does the heat death of the universe really imply a maximum entropy state *all* of the time? Or most of the time?

Statistically speaking, you're going to still encounter deviations from equilibrium, even though the expected value is equilibrium. But these rare deviations from equilibrium - which are inevitable - ...