Abstract
Bayesian theories of biological and brain function speculate that Markov blankets (a conditional independence separating a system from external states) play a key role for facilitating inference-like behaviour in living systems. Although it has been suggested that Markov blankets are commonplace in sparsely connected, nonequilibrium complex systems, this has not been studied in detail. Here, we show in two different examples (a pair of coupled Lorenz systems and a nonequilibrium Ising model) that sparse connectivity does not guarantee Markov blankets in the steady-state density of nonequilibrium systems. Conversely, in the nonequilibrium Ising model explored, the more distant from equilibrium the system appears to be correlated with the distance from displaying a Markov blanket. These result suggests that further assumptions might be needed in order to assume the presence of Markov blankets in the kind of nonequilibrium processes describing the activity of living systems.
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References
Aguilera, M., Di Paolo, E.A.: Integrated information in the thermodynamic limit. Neural Netw. 114, 136–146 (2019)
Aguilera, M., Igarashi, M., Shimazaki, H.: Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model. arXiv preprint arXiv:2205.09886 (2022)
Aguilera, M., Millidge, B., Tschantz, A., Buckley, C.L.: How particular is the physics of the free energy principle? Phys. Life Rev. (2022). https://doi.org/10.1016/j.plrev.2021.11.001
Aguilera, M., Moosavi, S.A., Shimazaki, H.: A unifying framework for mean-field theories of asymmetric kinetic Ising systems. Nat. Commun. 12(1), 1–12 (2021)
Biehl, M., Pollock, F.A., Kanai, R.: A technical critique of some parts of the free energy principle. Entropy 23(3), 293 (2021)
Crooks, G.E.: Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems. J. Stat. Phys. 90(5), 1481–1487 (1998)
Eyink, G.L., Lebowitz, J.L., Spohn, H.: Hydrodynamics and fluctuations outside of local equilibrium: driven diffusive systems. J. Stat. Phys. 83(3), 385–472 (1996)
Friston, K.: Life as we know it. J. R. Soc. Interface 10(86), 20130475 (2013)
Friston, K.: A free energy principle for a particular physics. arXiv preprint arXiv:1906.10184 (2019)
Friston, K.: Very particular: comment on “how particular is the physics of the free energy principle?’’. Phys. Life Rev. 41, 58–60 (2022)
Friston, K., et al.: The free energy principle made simpler but not too simple. arXiv preprint arXiv:2201.06387 (2022)
Friston, K., Heins, C., Ueltzhöffer, K., Da Costa, L., Parr, T.: Stochastic chaos and Markov blankets. Entropy 23(9), 1220 (2021)
Friston, K.J., Da Costa, L., Parr, T.: Some interesting observations on the free energy principle. Entropy 23(8), 1076 (2021)
Friston, K.J., et al.: Parcels and particles: Markov blankets in the brain. Netw. Neurosci. 5(1), 211–251 (2021)
Graham, R.: Covariant formulation of non-equilibrium statistical thermodynamics. Zeitschrift für Phys. B Condens. Matt. 26(4), 397–405 (1977)
Heins, C., Da Costa, L.: Sparse coupling and markov blankets: a comment on “how particular is the physics of the free energy principle?” By Aguilera, Millidge, Tschantz and Buckley. Phys. Life Rev. 42, 33–39 (2022)
Hipólito, I., Ramstead, M.J., Convertino, L., Bhat, A., Friston, K., Parr, T.: Markov blankets in the brain. Neurosci. Biobehav. Rev. 125, 88–97 (2021)
Ito, S., Oizumi, M., Amari, S.I.: Unified framework for the entropy production and the stochastic interaction based on information geometry. Phys. Rev. Res. 2(3), 033048 (2020)
Jarzynski, C.: Hamiltonian derivation of a detailed fluctuation theorem. J. Stat. Phys. 98(1), 77–102 (2000)
Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)
Parr, T., Da Costa, L., Heins, C., Ramstead, M.J.D., Friston, K.J.: Memory and Markov blankets. Entropy 23(9), 1105 (2021)
Pavliotis, G.A.: Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, vol. 60. Springer, Heidelberg (2014). https://doi.org/10.1007/978-1-4939-1323-7
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann (1988)
Richardson, T.S., Spirtes, P., et al.: Automated discovery of linear feedback models. Carnegie Mellon [Department of Philosophy] (1996)
Roudi, Y., Dunn, B., Hertz, J.: Multi-neuronal activity and functional connectivity in cell assemblies. Curr. Opin. Neurobiol. 32, 38–44 (2015)
Schnakenberg, J.: Network theory of microscopic and macroscopic behavior of master equation systems. Rev. Mod. Phys. 48(4), 571–585 (1976). https://doi.org/10.1103/RevModPhys.48.571
Seifert, U.: Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75(12), 126001 (2012)
Tomita, K., Tomita, H.: Irreversible circulation of fluctuation. Progress Theoret. Phys. 51(6), 1731–1749 (1974)
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Aguilera, M., Poc-López, Á., Heins, C., Buckley, C.L. (2023). Knitting a Markov Blanket is Hard When You are Out-of-Equilibrium: Two Examples in Canonical Nonequilibrium Models. In: Buckley, C.L., et al. Active Inference. IWAI 2022. Communications in Computer and Information Science, vol 1721. Springer, Cham. https://doi.org/10.1007/978-3-031-28719-0_5
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