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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How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...
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entropy of a long molecule chain with respect to its length

Consider a (very long) one-dimensional chain of $N$ moleculs, which can be in either of the energy states $\alpha$ or $\beta$. The configurations have length $a$ or $b$ respectively. Show ...
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86 views

Probability of spontaneous Boltzmann brain formation

I was reading through: http://www.scottaaronson.com/papers/giqtm3.pdf But I can't make sense of page 61 discussing Boltzmann brains. Specifically the fact that it says: But the problem is worse. ...
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Calculating entropy (heat exchange) [on hold]

This is a homework question. Suppose 30 gram of metal gallium melts at 36°C. The melting temperature is 29.9 °C and specific heat of fusion is 80.3 kJ/kg. Is the total change of entropy simply ΔS = ...
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Contradiction on Entropy of the “universe” decreasing

I have hit what seems to be a contradiction concerning entropy. In my class, we measured the entropy change of photosynthesis which is obviously a non-spontaneous process. We used the formula, ...
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Entropy / Structure Relations

I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? The further a system is from its maximum ...
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What is the conceptual difference between Gibbs and Boltzmann entropies?

In simple words what is the conceptual difference between Gibbs and Boltzmann entropies? Gibbs entropy: $S=-k_B\sum p_i\ln p_i$ Boltzmann entropy: $S=-k_B\ln \Omega$
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Calculating entropy [duplicate]

Suppose 30 gram of metal Gallium melts at 36 °C. The specific heat of fusion is 80.3 kJ/kg and the melting temperature is 29.9 °C. Explain if the melting of the Gallium in this process is ...
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30 views

Determine change in entropy - Please verify [closed]

Suppose 30 gram of metal gallium melts at 36°C. The melting temperature is 29.9 °C and specific heat of fusion is 80.3 kJ/kg. Explain if the melting of the gallium in this process is reversible or ...
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0answers
23 views

How much of elastic energy is stored as entropy?

There are two cases of elastic stretching: springs and rubber. When you streach a spring or a piece of rubber both absorb some energy as Entropy (S) and some as plain energy (U) $$\displaystyle{ ...
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0answers
39 views

Why doesn't this work? [closed]

Let us suppose that we have a machine. This machine produces energy in two ways: First it cools a supply of water down using refrigeration technology and sends the heat it collects to a heat ...
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1answer
114 views

Explicit form of the entropy production in hydrodynamics

I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the ...
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93 views

H-theorem and Boltzmann equation applied to Boltzmann distribution

Using the Boltzmann equation: $$ \frac{dH}{dt} = \int_0^{\infty} dr \int_0^{\infty} ds W(r,s)[p_r - p_s][\ln{p_r} - \ln{p_s}],$$ and assuming $p_r = e^{-\beta r}$, the equation looks like $$ ...
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35 views

Consequences of Entropy/Information Reversal in a System?

Can pairs of different physical systems be symmetrical under a process which would turn one of these physical system's entropic and informational contents into another system's respective ...
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What is the relationship between Energy, Entropy, and Information?

What is the relationship between Energy, Entropy, and Information? I read this - What Is Energy? Where did it come from? - and the top answer says that 'energy' is an abstract number that is a ...
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1answer
175 views

Is this derivation of Black Hole entropy viable?

This question is motivated by this one. Suppose $l$ is the minimum measurable unit of length. What is entropy of a spinless particle contained in this interval? We know that entropy of a two-level ...
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2answers
69 views

How can the microstates be measured with zero energy expenditure?

James P. Sethna. Statistical Mechanics. Exercise 5.2: What prevents a Maxwellian demon from using an atom in an unknown state to extract work? The demon must first measure which side of the ...
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158 views

Difference between irreversible and entropy?

Cedric Villani recently wrote an article on Landau damping, where at least one topic discussed confused me. Besides discussing the issue of how a process can be microscopically reversible and ...
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332 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...
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2answers
68 views

Why the amount of entropy increase to a system is less when heat is added to a higher temperature system than to a lower one?

As I understand it, statistically this means that a fall from a high temperature (say $300\text{ K}$) to a middle temperature ($200\text{ K}$), and an increase from say ($100\text{ K}$) to ($200\text{ ...
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2answers
148 views

Violation of the second law of thermodynamics? [closed]

Here is a machine which seems to violate the second law of thermodynamics: $A$ and $B$ are point black bodies of the same temperature (initially). everything is rotationally symmetric around the ...
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2answers
68 views

Modeling a list with a tunable degree of disorder/shuffling

Imagine we have a list of ordered numbers $L = (1, 2,\dots, N)$. I want to add an arbitrary amount of "disorder" to that list. For instance: Adding a little bit of disorder would permute a few ...
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6answers
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Why is information indestructible?

I really can't understand what Leonard Susskind means when he says that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He ...
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Isentropic and Isothermal Compressibility

Why isentropic compressibility is greater than isothermal compressibility ? While deriving $C_p$ and $C_v$ relation, I got $\frac{Cp}{Cv}$ as $\frac{ke}{Kt}$. Which tells us that $Ke > Kt$. But ...
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1answer
34 views

Unmixing of gases: What is the relevant temperature for my Entropy?

This answer to a question about unmixing gases states: However, let us now assume we have to hand a source of mechanical work, and a large heat reservoir at temperature $T$. I'll assume that ...
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34 views

Isentropic process and reversibility [duplicate]

I know that every adiabatic reversible process is an isentropic process. Can a process be isentropic but still not reversible adiabatic? Please provide me some examples.
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241 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
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1answer
19 views

How does entropy change when heat is transfer into a system reversibly with constant T?

My guess will be deltaS system : increase [because heat is flowing into the system] deltaS surrounding: decrease [because heat is leaving the environment] deltaS universe (sys+surr) : 0 because it ...
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2answers
130 views

Does entropy have a physical meaning?

Entropy is incredibly useful as a mathematical tool. But what does it actually mean? I understand that the Boltzmann entropy is defined by: $$S=k\ln{\Omega}$$ With $\Omega$ being the multiplicity ...
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39 views

For change in entropy dS = dq/T, is T the temperature of system or surrounding or both?

For change in entropy dS = dqrev/T, is T the temperature of system or surrounding or both? I am confused about Thot, Tcold, Tsys and Tsurr. If qrev, are we talking about the reversible cycle such as ...
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2answers
208 views

Is this theory about Universe and information true?

I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that ...
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35 views

Does the relation between entropy and temperature depend on the ensemble?

If we change the temperature of a given system, there will be a relation between its entropy and temperature S(T). Is S(T) the same in a canonical ensemble and a grand canonical ensemble? If not, is ...
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Definition of Entropy in thermodynamics

In most textbooks, the definition of entropy in reversible processes on a system $S$ is given simply as $$d S=\delta Q/T.$$ It seems to me this definition is insufficient since it does not specify ...
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What is entropy really?

On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as ...
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186 views

Entropy and the uncertainty principle

According to the second law of thermodynamics, the total entropy of the Universe must always increase after any interaction (as I understand). So in the hydrogen atom, the electron has a high ...
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109 views

“Violation” of the Second Law

I can't reconcile some facts about entropy and irreversibility. This depresses me, because I feel I can't quite grasp the importance of entropy. I will illustrate my problems with an example given by ...
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1answer
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Can you choose the variables of a state function?

I'm confused. I was first introduced to entropy as a state function of internal energy and volume $$S(U,V) \Rightarrow dS = C_v\frac{\mathrm{d}T}{T} - p\frac{\mathrm{d}V}{T} $$ wich is the ...
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Helmholtz free energy from a relation for entropy

The Legendre transformation defines the helmholtz free energy (at least according to my lectures) as: $F(T,V,N)=E-TS$ It also says to start with $E(S,V,N)$ and $T=\frac{\partial{E}}{\partial{S}}$ ...
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Has any possible non-extensive entropy been classified?

How many non-extensive entropies do exist? Tsallis, Havrda-Chavrat, Renyi, Kaniadakis, Sharma-Mittal,... To be more precise, I am wondering if some classification like those of "finite" or Lie groups ...
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1answer
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How to calculate the Wald functional?

I want to calculate the Wald functional for arbitrary higher curvature Lagrangians - like getting equation 6.31 from 6.30 in this paper. A priori the above looks like an extremely complicated ...
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5answers
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What is information?

We're all familiar with basic tenets such as "information cannot be transmitted faster than light" and ideas such as information conservation in scenarios like Hawking radiation (and in general, ...
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Entropy change at varying temperatures?

Entropy change is defined as the amount of energy dispersed reversibly to or from the system at a specific temperature. Reversivility means that the temperature of the system must remain constant ...
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4answers
194 views

Difference between heat capacity and entropy?

Heat capacity $C$ of an object is the proportionality constant between the heat $Q$ that the object absorbs or loses & the resulting temperature change $\delta T$ of the object. Entropy change is ...
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1answer
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Definition of entropy in nonequilibrium states

Thermodynamical definition of entropy $$S(p)=-\int p\ln p~dx$$ is defined only on equilibrium system. But why can't we use it for non-equilibrium system? Is there a well-accepted definition for it?
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Regarding the 'Arrow of Time'

I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their ...
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2answers
54 views

Thermodynamics of scattering theory

I have a couple of conceptual questions regarding the thermodynamics of scattering. Any partial answer or argument will be appreciated. For the sake of discussion, consider the scattering of ...
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83 views

Is there a minimum energy content of information, other than 0 Joules?

Lets say I want to send the bit string 010110 to someone. Is there a theoretical lower bound on the energy needed to do this?
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Axioms behind entropy!

The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory (Shannon entropy) up to its basic definition in statistical mechanics in terms of number of ...
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152 views

Is the second law of Thermodynamics an immense tautology?

Let's imagine for a second a system that is changing constantly from one microstate to another one. It could be a given volume of a gas with its atoms moving and bouncing around, or a deck of cards ...
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1answer
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Does the entropy of a system vary in the equilibrium?

I am not physicist and this question may seem trivial. But I understand that in the equilibrium the magnitudes such as temperature or volumen do not vary. Is the same for entropy? My logical says that ...