# THE PROBABILISTIC VIRTUES OF THE TEMPERATURE IN THE BAYESIAN BRAIN: Journaal of Neuroscience

*Tozzi A, Korbel J. The probabilistic virtues of the temperature in the bayesian brain (electronic response to: **Lee E, Seo M, Dal Monte O, Averbeck BB. Injection of a dopamine type 2 receptor antagonist into the dorsal striatum disrupts choices driven by previous outcomes, but not perceptual inference. **J Neurosci. 2015 Apr 22;35(16):6298-306. doi: 10.1523/JNEUROSCI.4561-14.2015).*

**THE PROBABILISTIC VIRTUES OF THE**** TEMPERATURE**** IN THE BAYESIAN BRAIN**

Arturo Tozzi, MD, PhD, AAP

Center for Nonlinear Science, University of North Texas, PO Box 311427, Denton, TX 76203-1427, USA

Jan Korbel

Dept. of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19, Prague 1, Czech Republic

The exciting paper from Lee et al. (Injection of a dopamine type 2 receptor antagonist into the dorsal striatum disrupts choices driven by previous outcomes, but not perceptual inference. J Neurosci. 2015 Apr 22;35(16):6298-306. doi: 10.1523/JNEUROSCI.4561-14.2015. https://www.jneurosci.org/content/35/16/6298.short) highlights the role of inverse temperature beta in charachterizing how consistently the animals chose the correct option after learning. If we take into account arguments concerning energy, it is possible to assess the correlations between temperature and bayesian choices driven by previous outcomes in another, underrated way. It is well known that increases or decreases in temperature, and thus in inverse temperature beta, lead to changes in thermodynamic entropy. The latter, in turn, displays close relationships - via the classical equation including the Boltzmann’s constant - with the Shannon’s microscopic informational entropy, which measures the uncertainty of a system, and with its elegant and useful generalization, the informational Rényi’s entropy, which is equipped with a so-called scalar exponent alpha (Jizba and Arimitsu, 2001). Because the inverse temperature beta and the Rényi’s exponent alpha exhibit a straight relation (Baez, 2011), therefore changes in temperature lead to different probability outcomes - in our case, to fluctuations of the statistical probability that a mental state occurs in a given conformation -. Indeed, information entropy and brain activity are closely related: it has been shown that the entropy is linked with different psychological and cognitive states. We will give some examples: analysis performed on emotionally online dialogues demonstrated the tendency towards a growing entropy (Sienkiewicz et al, 2013); ensemble of supervised maximum entropy classifiers can accurately detect and identify sentiments expressed in notes (Wicentowski and Sydes, 2012); further, perceptual functions are correlated with thermodynamical entropy and free energy (Freeman et al., 2011); Shannon’s entropy is able to predict task performance (Guastello et al., 2013). Finally, the entropy has been recently proposed as a measure of semantic and syntactic information of multidimensional discrete phenomena (Štys et al., 2015).

In conclusion, a clear link does exist between thermodynamic temperature and brain function evaluated in terms of probability states. Such a framework has the advantage of shedding new light on the fundamental challenge to understand the correlations between the psychological states and the brain equipped with a bayesian inferential machine (Friston, 2010): in some cases, the informational entropies –and in particular the Rényi’s entropy - allow us to evaluate the macrostates of the system based on the sole order parameter of the temperature, although we do not have a perfect knowledge of all the microstates.

**BIBLIOGRAPHY: **

*Baez JC (2011) Entropy and Free Energy. arXiv:1102.2098 [quant-ph]*

*Freeman WJ, Livi R, Obinata M, Vitiello G (2011) **Cortical phase transitions, non-equilibrium thermodynamics and the time-dependent Ginzburg-Landau equation. arXiv:1110.3677v1*

*Friston K** (2010)** The free-energy principle: a unified brain theory? Nat Rev Neurosci 11(2):127-138. doi: 10.1038/nrn2787*

*Guastello SJ, Gorin H, Huschen S, Peters NE, Fabisch M, et al. (2013) The minimum entropy principle and task performance. Nonlinear Dynamics, Psychology, and Life Science, 17(3):405-423*

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*Štys D, Korbel J, Rychtáriková R, Soloviov D, Císař P, Urban J (2015) Point information gain, point information gain entropy and point information gain entropy density as measures of semantic and syntactic information of multidimensional discrete phenomena. arXiv:1501.02891 *

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