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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Definition of the entropy

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) entropy of a variable $X$ is ...
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? [duplicate]

Take a box of gas particles. At $t = 0$, the distribution of particles is homogeneous. There is a small probability that at $t = 1$, all particles go to the left side of the box. In this case, entropy ...
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What is the entropy of a system when its volume tends to zero?

Say that a closed system has $n$ dimensions and is in the shape of a $n$-ball with a radius of 1, it's volume will be $$\frac{\pi^\frac{n}{2}}{\Gamma(\frac{n}{2}+1)}$$ which tends to 0 yet is not ...
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Mathematical proof of non-negative change of entropy $\Delta S\geq0$

I understand that we can prove that for any process that occurs in an isolated and closed system it must hold that $$\Delta S\geq0$$ via Clausius' theorem. My question is, how can I prove this in a ...
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Could entropy explain dark energy? [closed]

This was 3rd beer idea, so please bear with me. What if the universe was not actually expanding but the speed of light was slowing? Wouldn't that be indistinguishable to our observations? Either way ...
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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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Negative temperature and Absolute hot

This video explains that heat at negative temperatures flows from the negative object to the normal object. If the temperature of the normal object is absolute hot, what happens with the heat? The ...
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Would the universe get consumed by blackholes because of entropy?

Since the total entropy of the universe is increasing because of spontaneous processes, black holes form because of entropy (correct me if I'm wrong), and the universe is always expanding, would the ...
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Decrease in entropy in a fluid flow

Let's imagine a section of a pipe through which a fluid, gas for example, flows. When there is no pressure gradient, there is no flow. However, that does not mean that the molecules are at rest. They ...
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Integrating factor $1/T$ in 2nd Law of Thermodynamics

How would you prove that $1/T$ is the most suitable integrating factor to transform $\delta Q$ to an exact differential in the second law of thermodynamics: $$dS = \frac{\delta Q}{T}$$ Where $dS$ is ...
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167 views

Basic energy calculation for N identical spin system

We have a system that has N identical spins $n_i$, and each spin can be in state 1 or 0. The overall energy for the system is $\epsilon\sum_{i=1}^{N}n_i$. My understanding: There is only one ...
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Does entropy alter the probability of independent events?

So I have taken an introductory level quantum physics and am currently taking an introductory level probability class. Then this simple scenario came up: Given a fair coin that has been tossed 100 ...
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What happens at the interface between two universes with opposite thermodynamic arrows of time? [closed]

I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. ...
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Uncertainty and Thermodynamics

Dilemma The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that $\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
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Why does a temperature increase on a fixed volume increase entropy?

I heard that this statement is correct. However, it seems odd to me. The number of possible microstates is still the same, so isn't the entropy constant?
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Does entropy really always increase (or stay the same)? [duplicate]

Consider this image. If the big (grey) molecules were all to spontaneously move to the left, and the small ones were to move to the right, there would be an increase in order. While unlikely, ...
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Why is Entropy expressed in terms of Enthalpy?

Why does ${\Delta}S_{m(fusion)} = \frac{{\Delta}H_{m(fusion)}}{T}$ ? I always thought ${\Delta}S = \frac{dQ}{T}$ In this case does it mean $dQ = {\Delta}H$ ?? Why is it so?
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Is there a mechanism for time symmetry breaking?

Excluding Thermodynamic's arrow of time, all mathematical descriptions of time are symmetric. We know the arrow of time is real and we know the equations describing physics are real so is there any ...
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Von Neumann Entropy: varying definitions

I have seen different authors define von Neumann entropy in different ways. In particular, some use the natural logarithm and others log to base 2. What is the reasoning for this? Does it make any ...
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Difficulties with understanding total entropy change and unavailabillty

Of course, I know the fact that the entropy of an isolated system never decreases. Neverthless what makes me confused about the entropy(or change of entropy) of an isolated system is the explanation ...
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Why is the equation for Entropy of an ideal gas that undergoes reversible change in T at constant Pressure like this?

Why is the equation for change in Entropy for a reversible change in $T$ at constant $P$ described as $$\Delta S = n C_p \ln\frac{T_f}{T_i}$$
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Is there a relation between supersymmetry and entropy?

Considering that entropy denotes the level of order/disorder in a system, would it be possible for entropy and supersymmetry to exist at the same time? Or, are they entirely unrelated?
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Why isn't the Bekenstein-Hawking Entropy considered the quantum gravitational unification?

Based on the Bekenstein-Hawking Equation for Entropy, hasn't the relationship between quantum mechanics and gravity already been established.
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How to solve state parameters using these givens for an ideal gas?

In a thermodynamic turbine using air as an ideal gas, given that you have a known inlet temperature value $T_i$, a known exit pressure value $P_e$, a known inlet and exit velocity $V_i$ and $V_e$, a ...
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Do gasses always mix because of their Gibbs free energy?

As far as I know there are no two gasses that don't mix (excluding demixing by gravitational effects). For me, as someone working with fluids and surface tensions a lot, this means that the surface ...
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Entropy change relation to the number of lost bits

Can we use entropy change value to define the (perhaps fractional) number of bits of information that are lost by and, or, xor gates?
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How can dQ/T be interpreted as a system's level of disorder?

Long before statistical mechanics, entropy was introduced as: $dS = \frac{dQ}{T}$ At the time when entropy was introduced in this manner, was it known that entropy represents how "disordered" a ...
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Entropy and Crystal Growth

I was reading about growing single crystals and I'm a little confused about this - In most crystal growing processes, a "seed crystal" is used, and the rest of the material crystallizes on the seed ...
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What are the units of the Bekenstein bound?

Working with the Wikipedia definition of the Bekenstein bound: $S \leq \frac{2 \pi R k_bE}{\hbar c}$ $2\pi R \ $ is $m^2$ $k_b$ is $\frac{J}{K}$ $E$ is $J$ $\hbar$ is $J*s$ $c$ is $\frac{m}{s}$ ...
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Comments on entropy and the direction of time in Landau and Lifshitz's Statistical Mechanics

In Landau and Lifshitz's Stat Mech Volume I is the comment: However, despite this symmetry, quantum mechanics does in fact involve an important non-equivalence of the two directions of time. ...
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How to compute configurations (entropy) of a system?

If we have a system $X$ consisting of subsystems $X_1$ and $X_2$. We also know that $X_1$ and $X_2$ have eigenstates $H_1 = 1 \times 10^{20}$ and $H_2 = 1 \times 10 ^{22}$. Can we calculate the ...
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relation between first law of thermodynamics and statistical mechanics definition of entropy

From the definition of entropy as $S= - Tr (\rho\, ln \rho)$ one obtains that $S = \frac{\langle E \rangle}{T} + \log Z.$ The first law of thermodynamics has $dS = {dE \over T}$. Why is there no ...
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Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
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Entropy exchange of a free fall

I have a problem in which the tell me that you drop a bag of 50 kg of sand from 10 meters high, and you have to caltulate the entropy difference of the sand, asuming that the speific heat of the sand ...
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For an isolated system, can the entropy decrease or increase?

In any sizable system, the number of equilibrium states are much, much greater then the number of non-equilibrium states. Since each accessible micro state is equally probably, it is overwhelmingly ...
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Order = Energy = Mass?

Here is a following problem I encountered when chatting about physics with my friend: Let us imagine a classical example of ordered state of matter in thermodynamic sense: let's take a cylinder ...
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Can ice have a higher entropy than water?

I've leant that entropy is a state of randomness, and that solids have a more structured form, therefore having less entropy. However, I saw a YouTube comment stating the following: a liquid NOT ...
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The definition of entropy

As history of thermodynamics say, it was a mystery that what is the required condition for a given energy conversion to take place? Like there are two possible events each conserving energy but only ...
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Amount of energy to separate Gases - relationship to concentration

I want to understand the efficiencies of separating mixed gases, and for that I want to understand the thermodynamic limit case. Looking at the wikipedia page for entropy of mixing, I find the ...
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Isentropic Processes

I'm having trouble understanding why reversible adiabatic processes are isentropic. I understand that in a reversible adiabatic process there is no heat exchange and so $dQ = TdS = 0$. However, if ...
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Relation between Casimir and hydrophobic effects

Background Some years ago I was studying "Fundamentos de biología" (Biology fundamentals) and learned how the lipids create a bilayer due to the water repulsion. Some time later I learned that this ...
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Entropy Change During Reversible Processes

I'm confused about the Second Law of Thermodynamics. The Second Law of Thermodynamics prohibits a decrease in the entropy of a closed system and states that the entropy is unchanged during a ...
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Entalpy and entropy role in freezing-point depression phenomena

There's this "atomic" explanation of the freezing-point phenomena on Wikipedia that leaves me really intrigued. Consider the problem in which the solvent freezes to a very nearly pure crystal, ...
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Where and how is the entropy of a black hole stored?

Where and how is the entropy of a black hole stored? Is it around the horizon? Most of the entanglement entropy across the event horizon lies within Planck distances of it and are short lived. Is ...
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free energy and entropy of 2D soap froth

This is a (exploratory) computational project. The soap froth was created by injecting bubbles into a chamber formed by two rectangular plates which are 0.16cm. From the moment the soap froth was ...
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Entropy and the principle of least action

Is there any link between the law of maximum entropy and the principle of least action. Is it possible to derive one from the other ?
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How does quantum entropy scales with the size of the sample?

Suppose i have a 3D bulk of physical matter with no black holes enclosed in a sphere of radius $R$. What is the scaling law of all quantum entropy in function of $R$? If the scaling is not $R^2$, in ...
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Can entropy be equal to zero?

I've searched for it but I only found contradicting answers from "scientists": Dr. David Balson, Ph.D. states: "entropy in a system can never be equal to zero". Sam Bowen does not refutes the ...
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Why does the nature always prefer low energy and maximum entropy?

Why does the nature always prefer low energy and maximum entropy? I've just learned electrostatics and I still have no idea why like charges repel each other. ...
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name of experiment

I'm seeking the name of or reference for an experiment I once saw in a college physics class. At the beginning of one class the instructor repeatedly wound a wiper that spread a blot of some type of ...