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Proof of the H-theorem SupportiveArgument1 #105216

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The Arrow of Time »The Arrow of Time The Arrow of Time ☜A map exploring some issues concerning the nature of time that lie at the boundary of physics and philosophy. The map follows up a talk to the Blackheath Philosophy Forum on 2 April 2011 by Huw Price, Professor of Philosophy and director of the Center for Time at Sydney University.☜F1CEB7

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The physics of time »The physics of timeThe physics of time☜Is our subjective sense that time has a direction from past to future reflected in impersonal physical processes and laws? Is it better - from the impersonal viewpoint - to look asymmetries in time rather than a direction (to the future) of time?☜FFB597

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The thermodynamic arrow »The thermodynamic arrowThe thermodynamic arrow☜The Second Law of Thermodynamics implies an arrow of time in the sense that the entropy (or disorder) of an isolated system such as the whole universe never decreases - it either increases or remains constant.☜59C6EF

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Why do we see an entropy gradient? »Why do we see an entropy gradient?Why do we see an entropy gradient?☜We find ourselves in an observable universe in which entropy increases consistently in one direction, thereby showing time asymmetry - an arrow of time. Yet the vast majority of underlying dynamical processes are time-symmetric. How to account for this? Two broad approaches are considered here.☜FFB597

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Asymmetric physical processes »Asymmetric physical processesAsymmetric physical processes☜Various attempts have been made to explain increasing entropy by reference to asymmetries in physical processes - putative exceptions to the generalization that such processes are time-symmetric. Some suggested candidates are added below.☜59C6EF

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Bolztmann's H-theorem »Bolztmann's H-theoremBolztmann's H-theorem☜In his H-theorem Boltzmann tried to formally prove that inter-molecular collisions drive gases toward equilibrium, confirming the Second Law (for gases at least). In this approach, he aimed show that it is not just overwhelmingly probable but an exceptionless law like conservation of energy.☜9FDEF6

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Proof of the H-theoremProof of the H-theorem☜☜98CE71

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Assumption of molecular chaos »Assumption of molecular chaosAssumption of molecular chaos☜The H-theorem is invalidated by its reliance on a time-asymmetric assumption: the Stosszahlansatz (assumption of molecular chaos). This is the assumption that probabilities of velocities of colliding particles are independent.☜EF597B

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Link[1] Proof of the H-theorem (for the mathematically inclined)

Author: Wikipedia
Cited by: Peter Baldwin 7:48 AM 29 April 2011 GMT
URL:

http://en.wikipedia.org/wiki/H-theorem

Excerpt / Summary

"In Classical Statistical Mechanics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process. The H-theorem follows from considerations of Boltzmann's equation. It appears to predict an irreversible increase in entropy, despite microscopically reversible dynamics. This has led to much discussion."

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Entered by:- Peter Baldwin
NodeID: #105216
Node type: SupportiveArgument
Entry date (GMT): 4/29/2011 7:48:00 AM
Last edit date (GMT): 4/29/2011 7:48:00 AM
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