A Precise Formulation of the Third Law of Thermodynamics

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature I""(0) are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or ""by a finite number of operations""), it admits as corollary, under a continuity assumption, that all points of I""(0) are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.

On a uniform turnpike of the third kind in the Robinson-Solow-Srinivasan model

On using McKenzie’s taxonomy of optimal accumulation in the longrun, we report a “uniform turnpike” theorem of the third kind in a model original to Robinson, Solow and Srinivasan (RSS), and further studied by Stiglitz. Our results are presented in the undiscounted, discrete-time setting emphasized in the recent work of Khan-Mitra, and they rely on the importance of strictly concave felicity functions, or alternatively, on the value of a “marginal rate of transformation”, ξσ, from one period to the next not being unity. Our results, despite their specificity, contribute to the methodology of intertemporal optimization theory, as developed in economics by Ramsey, von Neumann and their followers.

Effect of the chronological age and sexual maturation on the time to exhaustion at maximal aerobic speed

The purposes of this study were: a) to verify the effect of chronological age and sexual maturation on the time to exhaustion at VO(2)max (t(lim)) and; b) to examine the reproducibility of t(lim) in boys aged 10-15 years. Forty boys, divided into 4 groups, in accordance to the chronological age (G10-12 and G13-15) and sexual maturation (P1-P3 and P4-P5 levels for pubic hair), performed the following tests: 1) incremental test for determination of VO(2)max and; 2) all-out exercise bout performed at VO(2)max to determine the t(lim). There was no difference of t(lim) (sec) between G10-12 and G13-15 (181.5 +/- 96.3 vs. 199 105.5). While the two measures of t(lim) were moderately related (r = 0.78), t(lim) from the second test (226.6 +/- 96.1 s) was higher than that of the first (191.3 +/- 79.2 s). We can conclude that the t(lim) is not influenced by chronological age and sexual maturation. Besides, t(lim) presents a lower reproducibility in children and adolescents.

Influence of nonsphericity of planetary satellites and perturbation of the third-body on the artificial satellites motion

Some orbital characteristics of lunar artificial satellites is presented taking into account the perturbation of the third-body in elliptical orbit and the non-uniform distribution of mass of the Moon. We consider the development of the non-sphericity of the Moon in zonal spherical harmonics up to the ninth order and sectorial harmonic C 22 due to the lunar equatorial ellipticity. The motion of the artificial satellite is studied under the single-averaged analytical model. The average is applied to the mean anomaly of the satellite to analyze low-altitude orbits which are of highest importance for future lunar missions. We found families of frozen orbits with long lifetimes for the problem of an orbiter travelling around the Moon.

Summary Record of the third Meeting Held at Havana, Cuba, on Tuesday, 7 June 1949, at 3.30 p.m.

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