São Paulo Research Foundation, Brazil | 2017 Dec 06
When galaxy clusters and globular star clusters form, a phenomenon called “violent relaxation” occurs. After interacting intensely, the thousands or even millions of bodies reach a state of relative gravitational equilibrium and a fairly long-lasting spatial distribution.
A new study by Brazilian researchers argues that astrophysicists’ understanding of violent relaxation is wrong and sets out to correct it. ...
“The relaxation process has always been analyzed using the Vlasov Equation... The problem is that Vlasov’s Equation assumes constant entropy in the system, meaning there’s no production of entropy. This is equivalent to saying the situation is symmetrical in time, since the arrow of time is determined by increasing entropy. It evidently isn’t in the actual phenomenon,” Sodré said.
If it were true, a process of this kind – reversible in time – would require a revision of the very foundations of physics. For this reason, the specialized literature refers to it as “the fundamental paradox of stellar dynamics”.
“It was clear to us that something was wrong, and our suspicion was confirmed by the study,” Sodré said. “The solution we found to the purported ‘paradox’ can be summed up in one short sentence: The Vlasov Equation simply doesn’t apply to this case.” ...
The Arrow of Time in the Collapse of Collisionless Self-Gravitating Systems:
Non-Validity of the Vlasov-Poisson Equation During Violent Relaxation - Leandro Beraldo e Silva et al