kole s. the arrow of time in cosmology and statistical physics

[...]... of other authors The discussion of the Second Law and the arrow of time being nished, I will procede in the next part with the arrow of time in cosmology 3.2 Cosmology and information theory In an article in Scienti c American 25], David Layzer presents an unorthodox theory concerning the arrows of time in both thermodynamics and cosmology He identi es two phenomenological arrows of time that are in. .. points according to the fundamental postulate of statistical mechanics at every instant in time The use of the postulate in this manner must rst be shown to be legitimate and is in fact in contradiction with the deterministic character of the underlying laws of dynamics Thirdly, the reasoning involved in establishing the statistical interpretation of the H -theorem is perfectly time symmetrical The. .. strong cosmological principle and of a prevailing thermodynamical equilibrium at or near the initial singularity, the historical and thermodynamical arrows of time will follow Many aspects of the derivation of Layzer remain unclear to me The most crucial point is, in my opinion, the absence of the connection between the cosmological and thermodynamical arrows of time It is one thing to prove, or make it... leave the H -theorem and other dynamical theories? According to Price, these theories incorporate somewhere a time asymmetrical principle (otherwise they cannot generate time asymmetrical results) and are aimed at explaining the future and not the past Since the real problem is not the entropy state of the future but that of the past, these theories are misdirected The only phenomenon that a dynamical theory... exist in the absence of the arrow of time of thermodynamics They call this the personal experience (in contrast with the scienti c experience) of the direction of time How to unite those two experiences? The second step in their line of arguments is to show that pure determinism is no longer a real possibility The prediction of the evolution of an ensemble would require an in nite amount of information... experience of time is the gearing of the electro-chemical processes in our brains to the purposeless drift into chaos as we sink into equilibrium and the grave." Atkins, P.W in 11, pp 88{90] 1.1 Introduction The negative picture inspiring Atkins to write these ominous words must have been the socalled \heat death" that awaits the universe as it evolves in time For when the Second Law of Thermodynamics... destruction, and the non-existence of prior states In the prior point of view one only applies the rerandomization posit (leading to higher entropy states) to initial states, and not the nal ones The latter point of view favors the correctness of statistical physics, in the sense that entropy should increase in both temporal directions, but the increase in one direction, the past, is excluded since the system... remains constant, due to Liouville's theorem This indicates the constancy of ne-grained entropy Since the trajectories of all representative points are time reversible, the ensemble construed 24 Time Asymmetry and the Second Law Fig 2.1: Time evolution of a system in phase space Fig 2.2: Time reversed evolution of a system in phase space by taking the time reversed states of all the points in the second... will therefore follow their analysis 3 Entropy and information are related by the fact that their sum remains equal 15 16 The Second Law The main argument runs as follows: proof that the equilibrium state is the most probable state of all states in which the system can reside (in the sense that the system will spend most of its time in this state in the in nite time limit), and then show that the system,...Chapter 1 The Second Law \We have looked through the window on the world provided by the Second law, and have seen the naked purposelessness of nature The deep structure of change is decay the spring of change in all its forms is the corruption of the quality of energy as it spreads chaotically, irreversibly, and purposelessly in time All change, and time' s arrow, point in the direction of corruption The