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[As requested, I convert my comment into an answer, as it might also be useful for other people.] There is a very interesting series of works by Lieb and Yngvason on entropy and the second law of thermodynamics, based on the kind of axiomatic approach you seem to be interested in. You can start with this introductory paper, or this, this or this more ...


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Now we have the second law of thermodynamics, that says that entropy always increases. Second law does not say exactly that. It has more formulations, some of which use the concept of entropy. One such formulation is When thermally insulated system changes its state from one equilibrium state to another, its entropy cannot decrease. This statement ...


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Are not we simply saying that things more likely to occur, occur more times? Isn't it then, that the second law is simply an inmense tautology? No, this argument doesn't suffice to prove the second law. This argument only proves that thermal fluctuations away from equilibrum should be rare and short-lived. That's a statement that doesn't have anything ...


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Ultimate physical motivation Strictly in the sense of physics, the entropy is less free than it might seem. It always has to provide a measure of energy released from a system not graspable by macroscopic parameters. I.e. it has to be subject to the relation $${\rm d}U = {\rm d}E_{macro} + T {\rm d} S$$ It has to carry all the forms of energy that cannot be ...


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Equilibrium is defined in the original notions of thermodynamics as the asymptotic static state. I.e., by this definition no macroscopical quantity varies in equilibrium. Statistical physics however tells us that the system varies in a certain "random walk" around all the possible states and never stops. We just cannot distinguish most of these states ...


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Thermodynamically entropy is defined by \begin{equation} \mathrm{d}S = \frac{\mathrm{d}Q_{rev}}{T} \, ,\end{equation} where $\mathrm{d}Q_{rev}$ is the heat, transferred reversibly. As you point out it can be shown that this quantity is a function of state. This implies that the entropy of any thermodynamic system has, up to a constant, a well defined ...


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A certain volume of space with a uniform distribution of particles has maximum entropy. That is correct for non-interacting particles, but wrong for particles with the gravitational interaction. When gravity condenses these particles, it increases the entropy of the system, not decreases it, at least when the Jeans instability condition is satisfied. ...


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Based on some "google research" I get the impression that the popularity of the perfume thought experiment stems from a 1975 Scientific American article written by David Layzer called The Arrow of Time. The article featured this figure visualizing the thought experiment: Of course, the notion that the second law of thermodynamics implies an asymmetry ...


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Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of information content, how can these two principles be compatible? I don't think there's anything inherently quantum-mechanical about this paradox. The same ...


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Prohibition of information destruction due to unitarity is a hypocrisy (sorry, I go to reiterate some stuff from the Where does deleted information go? posting), and the concept of entropy is foggy, especially in the quantum context: in spite of definitions mentioned in previous answers, there is no possibility to ever know the quantum state of a ...


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Henri Poincaré, in discovering limit cycles, used a thought experiment containing a box with a partition. One side had a gas, and the other didn't. When the partition was removed, the gas would diffuse through the opening and occupy both sides of the container. He first published works describing limit cycles somewhere in 1881-1882. I am unsure if he ...


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The Second Law of Thermodynamics states that the entropy of the universe always increases or stays constant. This means that we can reduce the entropy of the gas in the box (gas compressed from the whole box to half the box at constant temperature), only if we increase the entropy somewhere else. For example, we can compress the gas, doing work on it, and ...


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Can the law of conduction be derived from the assumptions of classical thermodynamics? The answer should be no, because classical thermodynamics does not deal with description of irreversible processes in time; it only deals with equilibrium states. Second law of thermodynamics does not assert that entropy decreases in time, only that after irreversible ...


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One cannot "derive" any non-equilibrium rate law from thermodynamics, simply because they are beyond the scope of the theory. Thermodynamics simply does not deal with such phenomena and hence cannot tell you how such processes occur (in this case heat conduction). All that thermodynamics does is relate mean values of certain properties of systems amongst ...


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Short answer is no but even then it depends on what you mean by "the 2nd law of thermodynamics". In conventional treatments of so-called equilibrium thermodynamics Fourier's law of heat conduction is completely independent of the rest. In what is called "rational thermodynamic" where the 2nd law is formulated as the "Clausius-Duhem inequality" it is in fact ...


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Conservation of information in quantum mechanics is a hypocrisy as much as it is so in classical mechanics. It is not conserved in the same sense as energy, charge, or momentum. When sages like Hawking and Penrose discuss whether does “information” survive destruction in a spacetime singularity, they mean something utterly different from the concept familiar ...


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No, the reasoning is wrong. When you need a N-qubit state, no difference entangled or not, you just initialize N qubits and then apply a unitary transformation (reversible). So, entropy produced during the initialization is proportional to the amount of information, without exponents.


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A reference that demonstrates the fact:'When a is a quantity with units (and b is dimensionless), it's perfectly valid to write alnb, but it is not equal to ln(ba), because ba is undefined and so is its logarithm.' I want to get more information/details that asserts the information you provided through your useful answer.


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Observer, if you assume as someone watching the experiment or activity, is plainly wrong. Anything that can be detected and measured and thus, in principle, from infinitely hard calculation can tell us about the past or previous states, can be said to be information, and thus, entropy increased while the process was being carried out. Take for example, a box ...


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To begin with, entropy is a classical thermodynamics concept. Different statistical frameworks , assuming some postulates, can define an entropy. The basic formulation of entropy defined by statistical mechanics where kB is the Boltzmann constant, equal to 1.38065×10^−23 J K−1. The summation is over all the possible microstates of the system, and p_i ...


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In quantum statistical mechanics entropy is not defined via the probability density of a single state but through the density matrix which talks about the "non-quantum uncertainty" over the states. This is the "probability density" over which all the entropy theorems are proven in the quantum world. That is, if we know the system to be in a sharp quantum ...


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I would strongly disagree with your statement that entropy has always been quite a mysterious quantity. Quite the contrary. What makes water (without something else interfering) always flow down the hill? Gravity. One does not have to know anything further about gravity to make good use of this statement, and people have used this fact for thousands of ...


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In classical thermodynamics only the change of entropy matters, $\Delta S = \int \frac{dQ}{T} $. At what temperature it is put zero is arbitrary. You have the similar situation with potential energy. One has to arbitrarily fix some point where the potential energy is put zero. This is because only differences of potential energy matters in mechanical ...


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What it means is that the number of bits required to specify the exact physical state the system is in, increases by 100/log(2) bits after the gas is heated. I think measuring the temperature in energy units is a step in the right direction, but what is even better is to do without any units. I.e. while units may be introduced for convenience, the formalism ...


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First, you have to understand that Rudolf Clausius put together his ideas on entropy in order to account for the losses of energy that was apparent in the practical application of the steam engine. At the time he had no real ability to explain or calculate entropy other than to show how it changed. This is why we are stuck with a lot of theory where we ...


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Entropy and 2nd law as disorder is a massive misunderstanding (propagated by prestigious physicists non-the less). In fact on this issue there are various physics schools of thought (and especially those of the thermodynamic flavor) which set this whole discussion on a new footing. It is shown that (for example in the work of Nobel-laurate I Prigogine) how ...


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Well i'm not into dark matter, but i am into entropy and stuff, so i will post an answer. How one is supposed to measure the entropy before and after, by counting micro-configurations, by counting volume/size, all these together? i suggest one or both of the above may give you an answer as to how the 2nd law may still be valid. No need for radiation (and ...


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Dark matter does not radiate photons by definition, but as I said in the comment to CuriousOne, dark matter may not have electromagnetic radiations to first order, but it does have gravitational radiation. The current Big Bang model accepts an effective gravitational interaction and thus the existence of gravitons, i.e. elementary particles of mass zero and ...


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A living organism is a very complex biological machine that seems to defy the laws of thermodynamics. The number of states a piece of matter forming a machine can be in in vastly less than if that piece of matter were in thermal and chemical equilibrium at ambient conditions. This means that machines cannot function for long if they can only interact with an ...


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The second law of thermodynamics is simply the definition of temperature. How does life, in your opinion, negate the existence of a thermodynamic temperature scale?


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A free dark matter cloud (without the presence of ordinary matter) will simply not "collapse" the same way a radiating gas cloud does. In both cases total momentum, angular momentum and energy are conserved, but in the case of a gas cloud the photons can carry away some of the angular momentum and most of the energy, in case of a dark matter cloud they ...


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I think the assumption that radiation is required for a collapse in general is mistaken. Think about a cloud of gas. If it is going to gravitationally collapse it must have a negative total energy; if it doesn't parts of the gas will fly off. If it has a negative total energy then there is some finite maximum size for the gas cloud, where it only has ...


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John Baez has a nice article on his website that goes into some detail on this question. Broadly, your intuition is right that at face value, it looks like structured systems are born out of nearly featureless initial conditions. However, as (for instance) a gas cloud collapses into a galaxy, it heats up (see the virial theorem, a theorem any ...


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Here's an intentionally more conceptual answer: Entropy is the smoothness of the energy distribution over some given region of space. To make that more precise, you must define the region, the type of energy (or mass-energy) considered sufficiently fluid within that region to be relevant, and the Fourier spectrum and phases of those energy types over that ...


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A higher entropy equilibrium state can be reached from the lower entropy state by an irreversible but purely adiabatic process. The reverse is not true, a lower entropy state can never be reached adiabatically from a higher entropy state. On a purely phenomenological level the entropy difference between two equilibrium states, therefore, tells you how "far" ...


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In terms of the temperature, the entropy can be defined as $$ \Delta S=\int \frac{dQ}{T}\tag{1} $$ which, as you note, is really a change of entropy and not the entropy itself. Thus, we can write (1) as $$ S(x,T)-S(x,T_0)=\int\frac{dQ(x,T)}{T}\tag{2} $$ But, we are free to set the zero-point of the entropy to anything we want (so as to make it convenient)1, ...


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As a general rule, physics gets easier when the mathematics gets harder. For example, algebra-based physics comprises a bunch of seemingly unrelated formulae, each and every one of which needs to be memorized separately. Add calculus and wow! Many of those supposedly disparate topics collapse into one. Add mathematics beyond the introductory calculus level ...


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You can set the entropy of your system under zero temperature to zero in compliance with the statistical definition $S=k_B\ln\Omega$. Then the S under other temperature should be $S=\int_0^T{\frac{dQ}{T}}$.


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The entropy of a system is the amount of information needed to specify the exact physical state of a system given its incomplete macroscopic specification. So, if a system can be in $\Omega$ possible states with equal probability then the number of bits needed to specify in exactly which one of these $\Omega$ states the system really is in would be ...


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The current entropy in the Universe is all stored in photons. The first reference by Qmechanic gives you the precise value. Since the photons of the CMBR do not at present interact with anything, the entropy of the Universe is very close to being a constant. What evolution there is, is all due to non-reversible processes in baryonic matter, but it amounts to ...


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If we assume our universe as an isolated system, then its entropy can only increase. It cannot decrease because of the second law of thermodynamics. It cannot stay unchanged because the universe is undergoing all kinds of irreversible processes.


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Strictly speaking, you're using the relation $a\ln b = \ln(b^a)$ outside of its domain of validity. When $a$ is a quantity with units (and $b$ is dimensionless), it's perfectly valid to write $a\ln b$, but it is not equal to $\ln(b^a)$, because $b^a$ is undefined and so is its logarithm. If you want, for notational convenience you could specify that the ...


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The entropy can be written as (discrete form)$$S=\sum_i p_ilog(p_i)$$ So you must identify what the uncertainty in your problem comes from, you would think that you have (in principle) exact deterministic equations for the evolution of these particles, so there is no uncertainty with respect to that. If you have unknown initial conditions then you could ...


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I'll make this an answer, even though it is more of a drawn out comment. As I mentioned as a comment, computing the potential energy is trivial. If you want speed, you'll probably want to look at fast methods for long-range interactions. The link takes you to state-of-the-art libraries and methods, but any introductory book on computational statistical ...


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Correct me if I am wrong, but a potential energy can only be determined for a conservative force field, which means that the force can only depend on position. So, because the charges vary with time you can not determine the potential energy. If the velocity is small compared to the oscillation, such that the displacement during the common period of the ...


1

Could anyone explain how this process complies with the second law of thermodynamics? The Stefan-Boltzmann law. I'll start with an ideal black body. Black bodies absorb all incoming radiation. They also emit radiation as a function of temperature. The peak frequency and the intensity increase as temperature increases. The emitted power is given by the ...


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Heat, in the context of something "giving off heat" that we use in everyday conversation, is a term we use often to describe emission of a specific part of the electromagnetic spectrum (namely the infrared spectrum). As you start to pour more and more energy into an object, the electrons can get more and more excited (which is the process of absorbing ...


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Regarding your new formulated question "my question boils down to whether a device similar to a voltmeter or thermometer exists for entropy": Well in that case then the answer is no, you can only measure entropy by studying the change of its dependencies on extensive/intensive variables that influence it (as they are different in different systems). To make ...



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