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I will start by answering the second question. Let's consider the case of two species of liquid in a box, with a partition separating them. The irreversible process you describe is to remove the partition. A reversible process would be to have the partition actually composed of two separate independently movable partitions. One of these does not interact ...

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This experiment is not possible, i.e. you cannot make a glass of only protons or a glass of only electrons because of the electromagnetic repulsion, they cannot be a liquid. A liquid requires chemistry They can be a gas though, and the LHC is creating a type of proton gas to get the protons for the beams. To get hydrogen gas into a plasma phase takes ...

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My understanding was always that this was a result of time evolution preserving measure in state space. So we have a space of states $\mathcal{P}$ with measure $\mu$ and there is an ensemble of states in $\mathcal{P}$ distributed according to some other measure $\nu$. We also have a dynamical system discribing time evolution $f:\mathcal{P} \times \mathbb{R} ... 4 It seems you're coming at entropy from a thermodynamics standpoint. This is completely consistent with (and, at the macro scale, equivalent to) the statistical derivation of entropy, but you might find the statistical version more intuitive, if the thermodynamic version is causing you issues. I warn you, statistical physics is both math-heavy and takes some ... 1 If you call$ \chi $the exergy (availability) then$ \chi = U + p_o V - T_o S $where$p_o, T_o$are the pressure and temperature of the environment (and are assumed to be constant). To find the maximum amount of useful work that can be extracted form the system it is sufficient to analyze reversible processes only so that$ dU=TdS-pdV $and then the exergy ... 1 The other thing that I can think of, is when you are not interested in some parts of your system(i.e. environment), so you trace it out. Now if the environment is not separable from the rest of the system, which is usually the case; what you are left with(the reduced state) is a mixed state. Note that in this case: $$\rho_{AB}\ne ... 0 According to our current scientific knowledge we know that we don't know what the 70% of the energy of the Universe is. Also, a comprehensive description of the thermodynamics of the Universe is impossible with the current standard Cosmological model and Einstein's General Relativity. In particular it's very complicated, and incomplete, as I said, to ... 0 For the limit of an infinite number of intermediate baths, we can make the approximation that T_\mathrm{bath} = T_\mathrm{block}, so for the bath: \delta S_\mathrm{bath} = \frac{\delta Q}{T_\mathrm{block}} = -\frac{C\delta T_\mathrm{block}}{T_\mathrm{block}} or d S_\mathrm{bath} = -\frac{C}{T_\mathrm{block}} d T_\mathrm{block} Note that \sum_{i= ... 1 I can't say I give this answer with great confidence, and I'll have to resort to some hand-waving. Think of the hydration shell around a hydrophobic substance. To minimize the local free energy, the water molecules will avoid any interaction with the hydrophobe and will seek to maximize attachment to the neighbouring water molecules, creating a sort of ... 0 I recently went to a colloquium with the theme "98 years of black hole physics" by string theorist Jan de Boer from the university of Amsterdam. I asked him this question and he replied that there have been lattice computations for black hole thermodynamics, yielding precisely Hawking's factor of 1/4. Furthermore the result has been obtained using ... 3 If you look at the first law of thermodynamics,$$dU=\delta Q-\delta W=TdS - pdV$$then consider a reversible processes (dU=0), then we get$$TdS=pdV$$Then using the ideal gas law, pV=nRT, we find$$ dS \sim \frac{dV}{V}$\$ The volume considered would be the volume of the system (e.g., a gas), with its infinitesimal increase(decrease) signified by ...

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See http://arxiv.org/abs/quant-ph/0512105. It gives a derivation of Landauer's Principle from the two postulates of the Second Law of Thermodynamics, and shows how Landauer's Principle follows from the second postulate.

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The problem is essentially the same problem as trying to define information entropy for a continuous probability distribution. You end up with an entropy value that has an offset depending on what units you chose for your random quantity. It is unfortunate, but the problem really stems from the fact that the number of possible physical states is uncountably ...

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Things become irreversible when you start ignoring certain degrees of freedom. What we call heat and friction is just our wilful ignorance of the trajectories of countless atoms. But the fact that the underlying equations of motion are time symmetric deals with microscopic phenomena. Sure, the time-reversed process is equally probable, which leads into the ...

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However, the simplest operations in computation, reset as well as the binary AND and OR operators, are irreversible. So? Their implementation in terms of CMOS logic is not irreversible, one can trackback the voltage levels. Sure, we can simulate irreversible systems with computers, but these aren't physically valid. However, because of the ...

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