Re: [AMBER-Developers] Relaxed, converged and equilibrated

From: B. Lachele Foley <>
Date: Fri, 5 Mar 2021 20:56:43 +0000

I have thought about this, too. I wonder if we could use something equivalent to a "confidence interval" in statistics. I think any such statement should include time as a qualifier. I don't really like the following, but it's a start - "the simulation is expected to have sampled X% of ensemble-appropriate phase space in the simulated time of Y seconds at 95% confidence". Has someone already done the math on this? I expect someone has.

This could help with the diamond-graphite issue. That is, one could say something like: the system is in equilibrium [at some stated conditions] at 99.999% confidence over an interval of Y million years with complete sampling occurring, on average, every Z milliseconds.

This sort of statistic would be very useful when people run multiple simulations for statistical or other purposes. Running multiple simulations improves sampling. But the sampling applies to a time length defined by the individual simulations (smallest? average? median?).

I do expect that someone has already done work on this. Do you know of it?

:-) Lachele

Dr. B. Lachele Foley (she/her/hers)
Associate Research Scientist
Complex Carbohydrate Research Center
The University of Georgia
Athens, GA USA
From: Adrian Roitberg <>
Sent: Friday, March 5, 2021 10:37 AM
To: <>
Subject: Re: [AMBER-Developers] Relaxed, converged and equilibrated


Not quite...

Feynman' example was for graphite vs diamond.

You can look at diamond essentially forever, with its own phonons
'equilibrated', but at longer time scales, probably > 10^15 years, it
MUST turn into graphite.

So, his fast and slow were for what we would call non-ergodic systems.

In our day to day simulations, if you have a protein that can
fold/unfold in milliseconds, the time scale separation gets trickier.


On 3/5/21 5:41 AM, Romain M. Wolf wrote:
> [External Email]
> I have no strong opinion on this either, but fully agree with Lachele's classification in a strict sense.
> Just thinking about the (funny?) definition of equilibrium from Richard Feynman's Statistical Mechanics course:
> "A system is in equilibrium when “all the fast things have happened but the slow things have not.”
> Applying this to an MD "equilibration" phase, we might argue that the system is "more or less in equilibrium" when all *very* fast things have happened, and all *slower* things are far from having happened.
> ...regards...romain
>> On 3 Mar 2021, at 08:31, B. Lachele Foley <> wrote:
>> I have no strong opinions on this, but others, notably Adrian, do. I want to make sure I have the same understanding of these words as others.
>> The following definitions are what I think others mean and are intended as a starting point for better definitions. Do you agree with them? If not, what should they be? Or what words would you give for these definitions? I tried to avoid deep stat-mech/thermo terminology.
>> Relaxed (commonly called 'equilibrated'):
>> In practical terms, the system has entered a stationary phase with respect to bulk properties that are expected to be in stationary phase per the simulation setup but that are not being held constant. These will typically include one or more of total energy, pressure, volume, density, and temperature. With respect to physics, this means that the simulated system has probably begun to sample configurations of mass and energy (momentum) in proportions consistent with the simulated ensemble (not necessarily the reality being modeled).
>> Converged:
>> For some property, not necessarily a bulk property, a stationary phase, which might unimodal or multimodal, has been sampled enough that meaningful statistical descriptions might be made about it. The system has sampled very well, in ensemble-appropriate proportions, a persistent or metastable subset of the phase space.
>> Equilibrated:
>> The entire system has sampled all available configurations sufficiently that meaningful statistics can be made about any system property. That is, the system has thoroughly sampled an ensemble-appropriate portion of the phase space, in ensemble-appropriate proportions, multiple times.
>> Most simulations of any significant complexity can only hope to attain 'converged' with respect to whatever properties are being tracked. It is very difficult to know for certain that other behaviors would not be observed were the simulation to be run longer. I think if there were an easy way to tell, then we would not very often need to do simulations. This problem also impacts our ability to know if 'relaxed' is truly 'relaxed', etc.
>> :-) Lachele
>> Dr. B. Lachele Foley (she/her/hers)
>> Associate Research Scientist
>> Complex Carbohydrate Research Center
>> The University of Georgia
>> Athens, GA USA
>> _______________________________________________
>> AMBER-Developers mailing list
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> AMBER-Developers mailing list

Dr. Adrian E. Roitberg
V.T. and Louise Jackson Professor in Chemistry
Department of Chemistry
University of Florida
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Received on Fri Mar 05 2021 - 13:00:02 PST
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