Home
»

ECEA-4
»
Section
f:
Astrophysics and Cosmology

# 4th International Electronic Conference on Entropy and Its Applications

# F: Astrophysics and Cosmology

The main areas of interest of this section are: Evolution of Stars, Gravitating Systems, Black Holes, The Universe.

This section is chaired by:

** Dr. Michael J. Way **

NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10027, USA

List of presentations (2)

Different notions of entropy can be identified in different communities [1]: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object – a black hole – having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form [2] is a positive quantity only comprising geometric attributes like an area A- which is the area of the event horizon of the black hole- , a length L_{P} – which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function [3] drawing on the phase-field concept of diffuse interfaces [4]. Entropy enters into the local, statistical description of contrast resp. gradient distributions in the transition region of the extended Heaviside function definition. The Bekenstein- Hawking formula structure can eventually be derived based on such geometric-statistic considerations.

- Haglund, J.; Jeppsson, F.; Strömdahl, H.: “Different Senses of Entropy—Implications for Education.” Entropy 2010, 12, 490-515.
- Bekenstein, J. D. (2008): Scholarpedia, 3(10):7375. doi:10.4249/scholarpedia.7375
- see e.g. : Weisstein, Eric W. "Heaviside Step Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HeavisideStepFunction.html
- see e.g. Provatas, N., Elder, K.: Phase-Field Methods in Materials Science and Engineering, Wiley VCH, Weinheim (2010),ISBN: 978-3-527-40747-7

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around $10^{123}k_B$ ($k_B$ being Boltzmann's constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of the Universe.

In a first approximation we model the cosmological fluid as the quantum probability fluid of free Schroedinger waves. We find that this model Universe saturates the holographic bound. As a second approximation we include the Hubble expansion of the galaxies. The corresponding Schroedinger waves lead to a value of the entropy lying three orders of magnitude below the holographic bound. Although a considerable improvement, this still lies above existing phenomenological estimates of the entropy of the Universe. Current work on a fully relativistic extension of our present model can be expected to yield results in even better agreement with empirical estimates of the entropy of the Universe.

List of Accepted Abstracts (1)

**Entropy production on exoplanets**
Although radiation in space is used to study exoplanets, entropy of radiation is not a parameter that has been considered for exoplanet studies. Nevertheless, entropy could be an interesting parameter to study the habitability conditions on exoplanets. In fact, on earth, entropy production is the reason for the presence of organised structures [Aoki, 1983] and living organisms feed on negative entropy from the surrounding environment [Schrödinger, 1944]. In this paper, we emphasise on the study of entropy flow and entropy productions on exoplanets along with energy of radiation. Net inflow of entropy on to a planet is always negative and the entropy flux (ds/dt) follows inverse proportionality with distance from star and albedo of planet and direct proportionality with the temperature of the parent star.

Following the idea in Aoki [1983], we present calculations for entropy production on exoplanets using the existing measured exoplanet parameters. The albedo of the planet is an important factor in determining the entropy production and effective temperature of the planet, and this parameter is not available yet for most of the exoplanets. In this work, we have calculated entropy production considering a range of albedos between 0 and 1, and we have identified those exoplanets which have entropy production similar to that of earth. Exoplanets with entropy production and size similar to that of earth could potentially form organised structures on its surface and atmosphere and could be good candidates to harbour life systems.

REFERENCES:

- Aoki, I. (1983). Entropy Productions on the Earth and Other Planets of the Solar System.
*Journal of the Physical Society of Japan*, 52(3), pp.1075-1078.
- Schrödinger, E. (1944).
*What is Life?*. London: Cambridge University Press.