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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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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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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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You pretty much got it right. "Live time" is often used in radiation detectors (both scintillator based and direct conversion) - or people sometimes use the converse, "dead time" (which is $1 - live time$). When you detect a radiation event, energy is deposited; it takes some time for this energy to be released and detected (either scintillator giving up ...


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The first thing that distinguishes a shock wave from an "ordinary" wave is that the initial disturbance in the medium that causes a shock wave is always traveling at a velocity greater than the phase velocity of sound (or light) in the medium. Notice that I said light - that is because there is also a kind of electromagnetic analogue to a shock wave known as ...


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When travelling in a dielectric light isn't light. It intracts with the medium to form a composite system that has an effective mass and therefore travels slower than $c$. If the interaction is strong, as in a BEC, the interacting system can be described as a quasiparticle called a polariton. This isn't useful for weakly interacting systems like most ...


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If you look at the 2 graphs, the force varies directly as the slope of the potential energy curve ($F\propto $ slope of $PE$)(or is it the other way around?). There is a reference to attraction in the PE graph because the atoms will stay together if the distance keeps the PE negative. If the distance were to decrease so that the PE is positive, the atoms ...


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What does negative potential energy mean here? Not much. The particular value of potential energy isn't important at all in classical physics. But changes in potential energy are. You could shift everything up so that $U>0$ everywhere, and you'd still get the same physics. (Why, you ask? Well, would the force change?) So why would people choose to ...


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In general, the absolute energy of a physical system does not matter for these potential problems. However, for convenience sake, one often choses to make the potential energy term at infinite separation equal to zero. If you were to hold the two atoms infinitely far away from each other, they will first experience an attractive force, because the ...


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While our definition of the meter is based on the speed of light, our definition of length is not. Naming and defining a unit of measurement is entirely different than defining a physical quantity. The most natural way to define distance (known by physicists as proper distance) is the measured spatial separation $\Delta r$ between two points in space. Rigid ...


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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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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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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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You're simply reading too much into the word "magnitude." You want to translate it into technical terminology as "absolute magnitude," since the latter is often abbreviated to "magnitude" by physicists anyway. But in everyday parlance "magnitude" is only trying to convey comparability. You have two things, each with their own magnitude, and the implication ...


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From a geometric object perspective, a scalar is a rank 0 tensor and, as such, is invariant under rotations of the coordinate system. The tensor contraction of, e.g., a one-form and a vector is a scalar, i.e., a real number.


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The dictionary definition is wrong. For example, time is a scalar in Newtonian mechanics, and time can be negative. That means that time is not completely specified by its magnitude (absolute value). Other examples include charge, energy, and Celsius temperature. The definition could be improved by cutting "is completely specified by its magnitude" and ...


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You must always say with respect to what something is a scalar. If we are given a group $G$, something is called a scalar if it is a member of the trivial representation of that group, i.e. if the (symmetry) group does nothing to it. Nothing more, nothing less. In the most common situation, this means that a scalar is a scalar under the rotation group ...


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The variable $r$ represents the position in space at which you wish to evaluate the wave function $\psi$. This is indicated by $\psi(r)$. The variable $r'$ is a spatial integration variable. It represents the points at which you are integrating the function $GV\psi$. An analogy to electrostatics might help. When you want to evaluate the electric potential ...


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When "year" is used as a unit for things unrelated to Earth's orbit, such as distances in light years or the age of the universe in years, it is the Julian year of exactly 365.25ยท86400 SI seconds.


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Which year? The sidereal year? The tropical year? The anomalistic year? The calendar year (and whose calendar)? The sidereal year is the average amount of time it takes the Earth to make one complete orbit about the Sun with respect to the fixed stars. The tropical year is the amount of average amount of time between successive spring equinoxes. The ...


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A year is defined by the time earth takes to circle the sun once: http://en.wikipedia.org/wiki/Year This does however not correspond to an even number of days. The SI unit of time is the second and $1\,\mathrm{day} = 24\cdot 3600\,\mathrm s$


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Fluctuations in the mean are also called fluctuations. It gives a notion about how reliable the mean value is (the second moment of the distribution). Any quantity that we are uncertain about will have that uncertainty encoded in a probability distribution, Quantum mechanics is no different in that respect then any other theory of inference, it is only ...



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