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Please use the preview button before saving. Jupiter, for instance, is still too hot for life to arise there for thousands of years, while the Moon is already too cold. The final state, in this view, is described as one of “equilibrium” in which all motion ceases. The three of them were said to have exchanged ideas on this subject. The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. 20th century and early 21st century. If the cosmological constant is zero, the universe will approach absolute zero temperature over a very long timescale.

With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long time scales. It is also possible that entropy production will cease and the universe will reach heat death. More recently, Grandy writes: “It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence. According to Tisza: “If an isolated system is not in equilibrium, we cannot associate an entropy with it. Buchdahl writes of “the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system”. According to Gallavotti: ” there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state. Discussing the question of entropy for non-equilibrium states in general, Lieb and Yngvason express their opinion as follows: “Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way.

These questions have a certain fascination, but the answers are speculations, and lie beyond the scope of this book. A recent analysis of entropy states that “The entropy of a general gravitational field is still not known,” and that “gravitational entropy is difficult to quantify. The analysis considers several possible assumptions that would be needed for estimates, and suggests that the visible universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor. It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. Such a system does not evolve toward a homogeneous equilibrium state.

Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems. Mr Joule’s equivalent of a Thermal Unit, and M. Proceedings of the Royal Society of Edinburgh for April 19, 1852, also Philosophical Magazine, Oct. Some Mathematical Aspects of Cosmology”. A dying universe: the long-term fate and evolution of astrophysical objects”. Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N.

Spontaneous Inflation and Origin of the Arrow of Time”. Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures. The book has gone through 11 editions, from 1897 until 1964, and still remains the most authoritative exposition of classical thermodynamics. T Press, Cambridge MA, p.