Historical and Physical Account on Entropy and Perspectives on the Second Law of Thermodynamics for Astrophysical and Cosmological Systems

Schoenmaker, J.

doi:10.3390/e16084420

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…Then, nearly ideal heat reservoirs would also fit the above description. The problem of working with ideal or nearly ideal heat reservoirs plays an important role in a number of not-well understood phenomena, or not-well-established dynamics, as in astrophysical and cosmological systems [19]. In such uncommon situations the simplification given by this geometrical interpretation may be of interest.…”

Section: An Application To Thermal Bathsmentioning

confidence: 99%

Equivalent norms in ${{\mathbb{R}}}^{n}$ from thermodynamical laws

González-Ayala¹,

Angulo‐Brown²

2015

Eur. J. Phys.

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In 1978, Landsberg proposed an elegant way of obtaining the inequality between arithmetic and geometric mean by using the first and second laws of thermodynamics. This result opened a debate on the logic legitimacy of this procedure to obtain some mathematical truths. Although this discussion can not be considered completed, the Landsberg approach has shown a great richness in obtaining many algebraic inequalities. In the present article we apply the Landsberg method to some properties of normed spaces trough a vector space of temperatures. In this way, the result that establishes the equivalence between all p-norms in the space n  and the minimal constant that guaranties this fact are readily found. Geometrical surfaces stemming from energy conservation are a consequence of this interpretation. In this manner, an application for thermal equilibrium of n reservoirs is suggested as an example of the contribution that the theory of norms may offer to physical problems when almost ideal heat baths are systems with a heat capacity of the form C aT m = with m  ¥. For this class of reservoirs the problem of obtaining the final temperature of two thermal baths with infinite or nearly infinite heat capacities in thermal contact is unambiguously solved. This might be the case in some systems which produce an incredibly large heat exchange due to small variations of temperature.

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Section: An Application To Thermal Bathsmentioning

confidence: 99%