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The physics and mathematics of the second law of thermodynamics

- E. Lieb, J. Yngvason
- Mathematics, Physics
- 26 August 1997

The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one… Expand

Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional

- E. Lieb, R. Seiringer, J. Yngvason
- Physics, Mathematics
- 26 August 1999

The ground-state properties of interacting Host gases in external potentials, as considered in recent exptriments, are usually described by means of the Gross-Pitaevskii energy functional. We present… Expand

The Mathematics of the Bose Gas and its Condensation

- E. Lieb, R. Seiringer, J. P. Solovej, J. Yngvason
- Mathematics, Physics
- 1 July 2005

The Dilute Bose Gas in 3D.- The Dilute Bose Gas in 2D.- Generalized Poincare Inequalities.- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases.- Gross-Pitaevskii Equation for Trapped… Expand

Ground State Energy of the Low Density Bose Gas

- E. Lieb, J. Yngvason
- Physics, Mathematics
- 12 December 1997

Now that the properties of low temperature Bose gases at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago.… Expand

Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

- E. Lieb, J. P. Solovej, J. Yngvason
- Physics
- 1 March 1994

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ→∞ in the following three regions:B≪Z4/3,B≈Z4/3 andZ4/3≪B≪Z3. In each case this is… Expand

The entropy concept for non-equilibrium states

- E. Lieb, J. Yngvason
- Mathematics, Physics
- Proceedings of the Royal Society A: Mathematical…
- 16 May 2013

In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation… Expand

Ground State Energy of the Low Density Bose Gas

- E. Lieb, J. Yngvason
- Physics
- 23 March 1998

Now that the properties of low temperature Bose gases at low density, ρ, can be examined exprimentally it is appropriate to revisit some of the formulas deduced by many authors four to five decades… Expand

A Fresh Look at Entropy and the Second Law of Thermodynamics

- E. Lieb, J. Yngvason
- Physics, Mathematics
- 24 March 2000

In days long gone, the second law of thermodynamics (which predated the first law) was regarded as perhaps the most perfect and unassailable law in physics. It was even supposed to have philosophical… Expand

A Rigorous Derivation¶of the Gross–Pitaevskii Energy Functional¶for a Two-dimensional Bose Gas

- E. Lieb, R. Seiringer, J. Yngvason
- Physics, Mathematics
- 1 May 2000

Abstract: We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when… Expand

A Guide to Entropy and the Second Law of Thermodynamics

- E. Lieb, J. Yngvason
- Mathematics, Physics
- 6 May 1998

This article is intended for readers who, like us, were told that the second law of thermodynamics is one of the major achievements of the nineteenth cenwry—that it is a logical, perfect, and… Expand

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