Thermal Physics

Decoherence has been the basis for understanding the emergence of the classical world from its quantum underpinnings. Unfortunately the calculations establishing decoherence overshoot and, based on assumptions that break down, predict that with the passage of time the off-diagonal elements of the density matrix become arbitrarily small. It has been recognized by some authors that the thermal state, assumed to hold for systems in equilibrium, places a bound on off diagonal terms. In this article we establish-preserving the conservation of energy, as is not the case for previous work-that indeed the thermal state is an attractor under scattering. Moreover, the bound on the off-diagonal terms present in the thermal state does not contradict everyday experience.

show abstract

“…with λ th the thermal wavelength [6]. Thus off-diagonal elements do decay, but have a finite distance scale.…”

Section: The Thermal Statementioning

confidence: 99%

Decoherence, the Density Matrix, the Thermal State and the Classical World

Gaveau

Schulman

2017

J Stat Phys

View full text Add to dashboard Cite

show abstract

“…The interviewer asked Joel to show where the Boltzmann factor came from before applying it to this situation, at which point Joel quoted the textbook derivation of the Boltzmann factor practically verbatim. The final portion of Baierlein's mathematical derivation is as follows [ [26,50], p. 92],…”

Section: B Recitation Of a Mathematical Derivation Without Physical mentioning

confidence: 99%

“…Furthermore, Joel had great difficulty relating the physical example used in the textbook (a "bit of cerium magnesium nitrate … in good thermal contact with a relatively large copper disc" (Ref. [26], p. 91) to the ideal gas example used during our interview. He was unable to recognize and articulate the important physical characteristics of each scenario that make the Boltzmann factor applicable, i.e., a system with fixed temperature and variable energy.…”

Section: B Recitation Of a Mathematical Derivation Without Physical mentioning

confidence: 99%

Student understanding of the Boltzmann factor

Smith

Mountcastle

Thompson

2015

Phys. Rev. ST Phys. Educ. Res.

View full text Add to dashboard Cite

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.

show abstract

“…which, when including also the configurational term (8) or (18), gives back the correct expression of the entropy of the (monoatomic) ideal gas:…”

Section: Update Of Velocitiesmentioning

confidence: 99%

The ideal gas as an urn model: derivation of the entropy formula

Prestipino

2004

Eur. J. Phys.

View full text Add to dashboard Cite

The approach of an ideal gas to equilibrium is simulated through a generalization of the Ehrenfest ball-and-box model. In the present model, the interior of each box is discretized, i.e., balls/particles live in cells whose occupation can be either multiple or single. Moreover, particles occasionally undergo random, but elastic, collisions between each other and against the container walls. I show, both analitically and numerically, that the number and energy of particles in a given box eventually evolve to an equilibrium distribution W which, depending on cell occupations, is binomial or hypergeometric in the particle number and beta-like in the energy. Furthermore, the long-run probability density of particle velocities is Maxwellian, whereas the Boltzmann entropy ln W exactly reproduces the ideal-gas entropy. Besides its own interest, this exercise is also relevant for pedagogical purposes since it provides, although in a simple case, an explicit probabilistic foundation for the ergodic hypothesis and for the maximum-entropy principle of thermodynamics. For this reason, its discussion can profitably be included in a graduate course on statistical mechanics.

show abstract

Thermal Physics

Cited by 142 publications

References 0 publications

Decoherence, the Density Matrix, the Thermal State and the Classical World

Decoherence, the Density Matrix, the Thermal State and the Classical World

Student understanding of the Boltzmann factor

The ideal gas as an urn model: derivation of the entropy formula

Contact Info

Product

Resources

About