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Wednesday, December 11th 2019

1:25 pm:

While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse settings. I will discuss how Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. The technique will be shown to reliably identify nonequilibrium phase transitions, determine their character, quantitatively predict dynamical critical exponents and correlation lengths without prior knowledge of the order parameters. I will show how CID revealed previously unknown ordering phenomena, such as a cascade of phase transitions in the BML traffic model, and a “checkerboard” dynamical instability in the parallel update Manna sandpile model. The scaling of the CID length scales agree well with those computed from the decay of two-point correlation functions g2(r) when they exist. But CID also reveals the correlation lengths scaling when g2(r) = 0, as we demonstrate by “cloaking” the data with a Rudin-Shapiro sequence. If time allows it, I will discuss preliminary results on how we can capture the local entropy production of an active Brownian particles system by compression.

References

[1] S. Martiniani, P. M. Chaikin, D. Levine, “Quantifying hidden order out of equilibrium”, Phys.

Rev. X, 9, 011031 (2019).

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