Some Special Instances of Entropy Change

2017 ◽  
pp. 144-148
Author(s):  
Alberto Gianinetti
Keyword(s):  
Statistical Mechanics ◽  
Fundamental Equation ◽  
Entropy Change ◽  
General Idea ◽  
Probable State

A few particular phenomena are quite difficult to frame into the fundamental equation, nonetheless they can be interpreted to the light of the general idea of statistical mechanics that any system and any overall change tend to the most probable state, i.e., a state that is microscopically equilibrated and then macroscopically stable.

scholarly journals Mixing indistinguishable systems leads to a quantum Gibbs paradox

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Benjamin Yadin ◽  
Benjamin Morris ◽  
Gerardo Adesso
Keyword(s):  
Statistical Mechanics ◽  
Thought Experiment ◽  
Entropy Change ◽  
Ideal Gas ◽  
Gibbs Paradox ◽  
Quantum Case ◽  
Entropy Increase ◽  
Level Of Knowledge ◽  
Different Gases ◽  
As If

AbstractThe classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an “ignorant” observer, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.

Boltzmann: the probabilistic interpretation of entropy

2020 ◽  
pp. 570-595
Author(s):  
Robert T. Hanlon
Keyword(s):  
Probability Theory ◽  
Statistical Mechanics ◽  
Gas Phase ◽  
Probabilistic Interpretation ◽  
Atoms And Molecules ◽  
Collective Work ◽  
Novel Approach ◽  
Probable State ◽  
Probable Distribution ◽  
Most Probable Distribution

Boltzmann’s collective work was a mathemetical tour de force. Building on Clausius and Maxwell, he demonstrated that the distribution of gas phase atoms and molecules follows from probability theory. Atoms and molecules distribute themselves in space and momentum to the most probable distribution. Boltzmann used probability theory to quantify the most probable state and then demonstrated the connection between this state and its entropy. This novel approach, later validated by Sackur–Tetrode, led to the creation of statistical mechanics.

Analytical representation of the adiabatic equation for detonation products based on statistical mechanics and intermolecular forces

1992 ◽  
Vol 339 (1654) ◽  
pp. 345-353 ◽  
Keyword(s):  
Equation Of State ◽  
Statistical Mechanics ◽  
Arbitrary Order ◽  
Fundamental Equation ◽  
Intermolecular Forces ◽  
Mathematical Form ◽  
Pentaerythritol Tetranitrate ◽  
Rational Approximants ◽  
Detonation Products ◽  
Reduced Density

A new mathematical form is presented for the equation of state of a detonation product fluid along the adiabat describing its expansion from the Chapman-Jouguet state. The basic ansatz is a rational function form for the adiabatic gamma coefficient in terms of the reduced density V cj /V as variable, from which the pressure can be derived analytically, and the internal energy by quadrature. Rational approximants of arbitrary order can be fitted by linear least squares to results from an ideal detonation code involving a fundamental equation of state based on statistical mechanics and intermolecular forces. The approximants can be checked for accuracy, and used in hydrodynamic codes. The method is illustrated by application to results for pentaerythritol tetranitrate, and the new equations are compared with the Jones-Wilkins-Lee equation.

Instances of Entropy Change

2017 ◽  
pp. 131-139
Author(s):  
Alberto Gianinetti
Keyword(s):  
Specific Interaction ◽  
Fundamental Equation ◽  
Entropy Change ◽  
Interaction Term

Entropy is maximal at equilibrium. According to the fundamental equation this demands that there is equilibration for every specific interaction term, namely, thermal, mechanical, diffusive, and others. Relevant exemplifications are illustrated for a number of important processes.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

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