Hawking-Bekenstein Entropy Nonsense

A not even wrong elaboration on Clausius' theorem:

http://www.scholarpedia.org/article/...awking_entropy
"The Bekenstein-Hawking entropy or black hole entropy is the amount of entropy that must be assigned to a black hole in order for it to comply with the laws of thermodynamics as they are interpreted by observers external to that black hole. [...] In ordinary thermodynamics the second law requires that the entropy of a closed system shall never decrease, and shall typically increase as a consequence of generic transformations. While this law may hold good for a system including a black hole, it is not informative in its original form. For example, if an ordinary system falls into a black hole, the ordinary entropy becomes invisible to an exterior observer, so from her viewpoint, saying that ordinary entropy increases does not provide any insight: the ordinary second law is transcended. Including the black hole entropy in the entropy ledger gives a more useful law, the generalized second law of thermodynamics (GSL) (Bekenstein 1972, 1973, 1974): the sum of ordinary entropy So outside black holes and the total black hole entropy never decreases and typically increases as a consequence of generic transformations of the black hole. In equations ΔSo + ΔSBH ≥ 0."

Most probably neither Stephen Hawking nor Jacob Bekenstein has ever known that the version of the second law stated as "Entropy always increases" (which, according to A. Eddington, holds "the supreme position among the laws of Nature") is in fact a theorem deduced by Clausius in 1865:

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 37: "Hence we obtain: THE ENTROPY PRINCIPLE (Clausius' version) For every nicht umkehrbar [irreversible] process in an adiabatically isolated system which begins and ends in an equilibrium state, the entropy of the final state is greater than or equal to that of the initial state. For every umkehrbar [reversible] process in an adiabatical system, the entropy of the final state is equal to that of the initial state."

Clausius' deduction was based on three postulates:

Postulate 1 (implicit): The entropy is a state function.

Postulate 2: Clausius' inequality (formula 10 on p. 33 in Uffink's paper) is correct.

Postulate 3: Any irreversible process can be closed by a reversible process to become a cycle.

All the three postulates remain unproven even nowadays; Postulate 3 is almost obviously false:

Uffink, p.39: "A more important objection, it seems to me, is that Clausius bases his conclusion that the entropy increases in a nicht umkehrbar [irreversible] process on the assumption that such a process can be closed by an umkehrbar [reversible] process to become a cycle. This is essential for the definition of the entropy difference between the initial and final states.. But the assumption is far from obvious for a system more complex than an ideal gas, or for states far from equilibrium, or for processes other than the simple exchange of heat and work. Thus, the generalisation to all transformations occurring in Nature is somewhat rash."

Note that, even if Clausius' theorem were correct (it is not), it only holds for "an adiabatically isolated system which begins and ends in an equilibrium state". Do processes Hawking and Bekenstein consider "begin and end in an equilibrium state"?

Hawking-Bekenstein entropy nonsense is one of the worst examples of not even wrongness in today's science. There is a general feeling that science is dying, many scientists raise the alarm, but the process is perhaps irreversible:

http://www2.macleans.ca/2013/09/05/p...odern-physics/
Neil Turok: "It's the ultimate catastrophe: that theoretical physics has led to this crazy situation where the physicists are utterly confused and seem not to have any predictions at all."

http://www.math.columbia.edu/~woit/wordpress/?p=7266
Peter Woit: "As far as this stuff goes, we're now not only at John Horgan's "End of Science", but gone past it already and deep into something different."

http://archipope.over-blog.com/article-12278372.html
"Nous nous trouvons dans une période de mutation extrêmement profonde. Nous sommes en effet Ã* la fin de la science telle que l'Occident l'a connue », tel est constat actuel que dresse Jean-Marc Lévy-Leblond, physicien théoricien, épistémologue et directeur des collections scientifiques des Editions du Seuil."

Pentcho Valev

Is the second law of thermodynamics true after all? One thing is su The scientific community would pay no attention to any evidence showing that the law is false, even if this evidence is published in a prestigious journal:

http://scitation.aip.org/content/aip...1063/1.4825269
Electricity generated from ambient heat across a silicon surface, Guoan Tai, Zihan Xu, and Jinsong Liu, Appl. Phys. Lett. 103, 163902 (2013): "We report generation of electricity from the limitless thermal motion of ions across a two-dimensional (2D) silicon (Si) surface at room temperature. [...] ....limitless ambient heat, which is universally present in the form of kinetic energy from molecular, particle, and ion sources, has not yet been reported to generate electricity. [...] This study provides insights into the development of self-charging technologies to harvest energy from ambient heat, and the power output is comparable to several environmental energy harvesting techniques such as ZnO nanogenerator, liquid and gas flow-induced electricity generation across carbon nanotube thin films and graphene, although this remains a challenge to the second law of thermodynamics..."

https://www.scientificexploration.org/edgescience/24
Daniel P. Sheehan, Beyond the Second Law of Thermodynamics: "These culminated in 2012-13 with a series of laboratory experiments that showed true second law breakdown. The demonstration was straightforward. A small, closed, high- temperature cavity contained two metal catalysts (rhenium and tungsten), which were known to dissociate molecular hydro- gen (H2) to different degrees (Figure 1). (Rhenium dissociates hydrogen molecules into atoms better than tungsten does; conversely, tungsten recombines hydrogen atoms back into hydrogen molecules better than rhenium.) Because the dissociation reaction (H2 - 2H) is endothermic (absorbs heat), and the recombination reaction (2H - H2) is exothermic (liberates heat), when hydrogen was introduced into the cavity, the rhenium surfaces cooled (up to more than 125 K) relative to the tungsten (Figure 2). Because the hydrogen-metal reactions were ongoing in the sealed cavity, the rhenium stayed cooler than the tungsten indefinitely. This permanent temperature difference--this steady-state nonequilibrium--is expressly forbidden by the second law, not just because the system won't settle down to a single-temperature equilibrium, but because this steady-state temperature difference can, in principle, be used to drive a heat engine (or produce electricity) solely by converting heat back into work, which is a violation of one of the most fundamental statements of the second law (Kelvin- Planck formulation)."

http://arxiv.org/abs/1203.0161
Self-Charged Graphene Battery Harvests Electricity from Thermal Energy of the Environment, Zihan Xu et al: "Moreover, the thermal velocity of ions can be maintained by the external environment, which means it is unlimited. However, little study has been reported on converting the ionic thermal energy into electricity. Here we present a graphene device with asymmetric electrodes configuration to capture such ionic thermal energy and convert it into electricity. [...] To exclude the possibility of chemical reaction, we performed control experiments... [...] In conclusion, we could not find any evidences that support the opinion that the induced voltage came from chemical reaction. The mechanism for electricity generation by graphene in solution is a pure physical process..."

And since scientists are not interested in whether the second law of thermodynamics is true or false, they simply couldn't care less about the fact that the second law is ill-defined, to say the least:

http://philsci-archive.pitt.edu/archive/00000313/
Jos Uffink: "Snow stands up for the view that exact science is, in its own right, an essential part of civilisation, and should not merely be valued for its technological applications. Anyone who does not know the Second Law of Thermodynamics, and is proud of it too, exposes oneself as a Philistine.. Snow's plea will strike a chord with every physicist who has ever attended a birthday party. But his call for cultural recognition creates obligations too. Before one can claim that acquaintance with the Second Law is as indispensable to a cultural education as Macbeth or Hamlet, it should obviously be clear what this law states. This question is surprisingly difficult. The Second Law made its appearance in physics around 1850, but a half century later it was already surrounded by so much confusion that the British Association for the Advancement of Science decided to appoint a special committee with the task of providing clarity about the meaning of this law. However, its final report (Bryan 1891) did not settle the issue. Half a century later, the physicist/philosopher Bridgman still complained that there are almost as many formulations of the second law as there have been discussions of it. And even today, the Second Law remains so obscure that it continues to attract new efforts at clarification. [...] The historian of science and mathematician Truesdell made a detailed study of the historical development of thermodynamics in the period 1822-1854. He characterises the theory, even in its present state, as 'a dismal swamp of obscurity' and 'a prime example to show that physicists are not exempt from the madness of crowds'. (...) Clausius' verbal statement of the second law makes no sense.... All that remains is a Mosaic prohibition ; a century of philosophers and journalists have acclaimed this commandment ; a century of mathematicians have shuddered and averted their eyes from the unclean.... Seven times in the past thirty years have I tried to follow the argument Clausius offers... and seven times has it blanked and gravelled me.... I cannot explain what I cannot understand."

Pentcho Valev