The unattainability formulation of the Third Law of Thermodynamics is briefly reviewed. Purely dynamic – as opposed to thermodynamic – limitations on the quest for absolute Abstract We consider first the absolute zero of temperature and then negative Kelvin temperatures. (S not E denotes entropy in TSRR and CSRR, and E denotes energy in ERR, because S is the standard symbol for entropy, and E for energy.) With respect to both TSRR and CSRR, we consider not only the issue of attainability of absolute zero, but also the separate issues, even if absolute zero can be attained, of maintaining it, and of verifying that it has been attained. We also briefly consider energy-reduction refrigeration (ERR), which entails extraction of energy but not entropy from a refrigerated system, and quantum-control refrigeration (QCR). Or, in other words, the Second law of Thermodynamics requires any localization in the total momentum-plus-position phase space of a refrigerated system to be paid for by a compensating greater (in the limit of perfection, equal) delocalization in the total momentum-plus-position phase space of the refrigerated system and/or of its surroundings. Of course, the Second Law of Thermodynamics requires any decrease in entropy of a refrigerated system to be paid for by a compensating greater (in the limit of perfection, equal) increase in eLtropy. CSRR entails reduction of a refrigerated system's configurational entropy, i.e., its localization in position space, via positional isolation of entities that happen to be in their ground states. (In standard TSRR, refrigeration is achieved at the expense of work input in absorption TSRR, at the expense of high-temperature heat input.) We then consider the possibility or impossibility of the attainability of absolute zero temperature via configurational-entropy-reduction refrigeration (CSRR). The possibility or impossibility of overcoming these limitations via TSRR is considered, with respect to both standard and absorption TSRR. TSRR entails reduction of a refrigerated system's thermal entropy, i.e., its localization in momentum space. But typically it is stated principally with respect to thermal-entropy-reduction refrigeration (TSRR). It puts limitations on the quest for absolute zero, and in its strongest mode forbids the attainment of absolute zero by any method whatsoever. We consider first the absolute zero of temperature and then negative Kelvin temperatures.
The averaged relative energy density is positive definite for the all Friedman and other universes which have been considered The obtained results are interesting, e.g.,
Momentum of the Friedman (and also more general, only homogeneous) universes. The averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and Tensors, to coordinate independent analysis (local and in special cases also global) of this field. Of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum The averaged relative energy–momentum and angular momentum tensors Tensors and they depend on some fundamental length L > 0. These tensors are very closely related to the canonical superenergy and angular supermomentum We have called these tensorial quantities “the averaged relative energy–momentumĪnd angular momentum tensors”. The energy–momentum and angular momentum densities. Of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of
In this paper we present another averaging One of these averaging was used in our papers giving the canonical superenergy and angular supermomentum tensors. The obtained averaged quantities are equivalent mathematically because they differ onlyīy constant scalar dimensional factors. There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates
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