Inducing time-asymmetry on reversible classical statistical mechanics via Interventional Thermodynamic Ensembles (ITEs).

Preamble 

Probably, one of the most fundamental issue in classical statistical mechanics is extending reversible dynamics to many-particle systems that behaves irreversibly. In other words, how time's arrow appears even though constituted systems evolves in reversible dynamics. This is the main idea of Loschmidt's paradox. The resolution to this paradox lies into something called interventional thermodynamic ensembles (ITEs).  

Leaning Tower
of Pisa:Recall Galileo's 
Experiments
 (Wikipedia)

Time-asymmetry is about different histories : Counterfactual dynamics

Before trying to understand how ITEs are used in resolving Loschmidt's paradox, we understand that inducing different trajectories on an identical dynamical system in "a parallel universe" implies time-asymmetry. A trajectory provides here a reversibility.  So called "a parallel universe" is about imagining a different dynamics via a sampling, this corresponds to counterfactuals within Causal inference frameworks. 

Interventional Thermodynamic Ensembles (ITEs)

Interventional ensemble build upon an other ensemble, for the sake of simplicity, we can think of an ensemble as an associated chosen sampling scheme. From this perspective,  sampling scheme $\mathscr{E}$ would have an interventional sampling $do(\mathscr{E})$ if the adjusted scheme only  introduces a change in the scheme that doesn't change the inherent dynamics but effects the dynamical  history. One of the first examples of this is appeared recently: single-spin-flip vs. dual-spin-flip dynamics [suezen23]. This is shown with simulations. 

Outlook

Reversibility and time-asymmetry in classical dynamics are a long standing issues in physics. By inducing causal inference perspective in computing dynamical evolution of many body systems leads to reconciliation of reversibility and time-asymmetry i.e., $do-$operator's interpretation.

References

[suezen23] H-theorem do-conjecture (2023) arXiv:2310.01458 (simulation code GitHub).

Please Cite as:

 @misc{suezen24ite, 

     title = {Inducing time-asymmetry on reversible classical statistical mechanics via  Interventional Thermodynamic Ensembles (ITEs)}, 

     howpublished = {\url{https://memosisland.blogspot.com/2024/02/inducing-time-asymmetry-on-reversible.html}, 

     author = {Mehmet Süzen},

     year = {2024}

}  

Exact reproducibility of stochastic simulations for parallel and serial algorithms simultaneously Random Stream Chunking

Preamble 

Figure: Visual description of
random stream chunking, M.Suzen (2017)

The advent of using computational sciences approaches, i.e., data science and machine learning, in the industry becomes more common practice in almost all organisations due to the democratisation of data science tools and availability of inexpensive cloud infrastructure. This brings the requirement or even compulsory practice of a code being so called parallelised. Note that parallelisation is used as an umbrella term here for using multiple compute resources in accelerating otherwise a serial computation and could mean a distributed or multi-core computing, i.e., multiple CPUs/GPUs. Here we provide a simple yet a very powerful approach to preserve reproducibility of parallel and serial implementation of the same algorithm that uses random numbers, i.e., stochastic simulations. We assume Single Instruction Multiple Data (SIMD) setting. 

Terminology on repeatability, reproducibility and  replicability 

Even though we only use reproducibility as a term as an umbrella term, there are clear distinctions, recommended by ACM, here. We summarise this from computational science perspective :

repeatability : Owner re-run the code to produce the same results on own environment. 

reproducibility: Others can  re-run the code to produce the same results on other's environment. 

replicability: Others can re-code the same thing differently and produce the same results on other's environment. 

In the context of this post, since parallel and serial settings would constitute different environments, the practice of getting the same results, this falls under reproducibility.   

Single Instruction Multiple Data (SIMD) setting. 

This is the most used, and probably the only one you would ever need, approach in parallel processing. It implies using the same instruction, i.e., algorithm or function/module, for the distinct portions of the data. This originates from applied mathematics techniques so called domain decomposition method. 

Simultaneous Random Stream Chunking 

The approach in ensuring exact reproducibility of a stochastic algorithm in both serial and parallel implementation lies in default chunking in producing the random numbers both in serial and parallel code. This approach used in the Bristol Python package Here is the mathematical definition. 

Defintion Random Stream Chunking Given a random number generator $\mathscr{R}(s_{k})$ with as seed $s_{k}$ is used over $k$-partitions. These partitions are always corresponds to $k$ datasets, MD portion of SIMD. In the case of parallel algorithms, each $k$ corresponds to a different compute resource     $\mathscr{C}_{k}$. 

By this definition we ensure that both parallel and serial processing receiving exactly the same random number, this is summarised in the Figure.

Conclusion

We outline a simple yet effective way of ensuring exact reproducibility of serial and parallel simulations simultaneously. However, reproducibility of stochastic simulations are highly hardware dependent as well, such as GPUs and NPUs, and their internal streams might not be that easy to control partitions, but generic idea presented here should be applicable.

Please cite this article as: 

 @misc{suezen24rep, 

     title = {Exact reproducibility of stochastic simulations for parallel and serial algorithms simultaneously}, 

     howpublished = {\url{https://memosisland.blogspot.com/2024/02/exact-reproducibility-of-stochastic.html}, 

     author = {Mehmet Süzen},

     year = {2024}

}