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A Connection from Thermodynamics and Information Theory HYPOTHESIS AND THEORY published: 16 June 2015 doi: 10.3389/fpsyg.2015.00818 Brain activity and cognition: a connection from thermodynamics and information theory Guillem Collell 1 and Jordi Fauquet 2, 3* 1 Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA, 2 Department of Psychobiology and Methodology of Health Sciences, Universitat Autònoma de Barcelona, Barcelona, Spain, 3 Research Group in Neuroimage, Neurosciences Research Program, Hospital del Mar Medical Research Institute, Barcelona Biomedical Research Park, Barcelona, Spain The connection between brain and mind is an important scientific and philosophical question that we are still far from completely understanding. A crucial point to our work is noticing that thermodynamics provides a convenient framework to model brain activity, whereas cognition can be modeled in information-theoretical terms. In fact, several models have been proposed so far from both approaches. A second critical remark is Edited by: Joan Guàrdia-olmos, the existence of deep theoretical connections between thermodynamics and information University of Barcelona, Spain theory. In fact, some well-known authors claim that the laws of thermodynamics are Reviewed by: nothing but principles in information theory. Unlike in physics or chemistry, a formalization Enrique Hernandez-Lemus, of the relationship between information and energy is currently lacking in neuroscience. National Institute of Genomic Medicine, Mexico In this paper we propose a framework to connect physical brain and cognitive models by Antonio Hervás-Jorge, means of the theoretical connections between information theory and thermodynamics. Universitat Politecnica de Valencia, Spain Ultimately, this article aims at providing further insight on the formal relationship between *Correspondence: cognition and neural activity. Jordi Fauquet, Keywords: free energy, negentropy, brain thermodynamics, cognitive models, information theory Department of Psychobiology and Methodology of Health Sciences, Campus de la Universitat Autònoma de Barcelona, Edifici B, 08193 Introduction Bellaterra, Barcelona, Spain [email protected] The brain is a thermodynamic device aimed at processing information. Consequently, brain activity has often been modeled in thermodynamic terms (La Cerra, 2003; Varpula et al., 2013) and Specialty section: cognitive processes in information terms (Anderson, 1996; Friston, 2010). These two different This article was submitted to approaches, separately, yield accurate descriptions of brain and cognitive processes. However, Quantitative Psychology and their unification would greatly increase our understanding of how brain activity is related to Measurement, cognition and in turn would benefit both perspectives (Collell and Fauquet, 2014). Critically, a section of the journal there are deep theoretical connections between information theory and thermodynamics. Some Frontiers in Psychology of the classical links between the two disciplines are the Landauer limit (Landauer, 1961), the Received: 25 March 2015 energetic cost of processing information (Bennett, 1982), the Gibbs and Boltzmann formulas Accepted: 29 May 2015 and the concepts of entropy and negentropy (Schrodinger, 1944; Brillouin, 1953). Interestingly, Published: 16 June 2015 entropy is a central concept in both information theory and thermodynamics. Even though it is Citation: a measure of a different quantity in each theory, these quantities exhibit important theoretical Collell G and Fauquet J (2015) Brain activity and cognition: a connection relationships, as will be discussed below. In fact, several authors suggested that the relationship from thermodynamics and information between thermodynamics and information theory is even stronger and claim that the laws of theory. Front. Psychol. 6:818. thermodynamics are nothing but theorems in information theory (Rothstein, 1951; Brillouin, doi: 10.3389/fpsyg.2015.00818 1953). Notably, the aforementioned connections can serve as a set of powerful tools to unify Frontiers in Psychology | www.frontiersin.org 1 June 2015 | Volume 6 | Article 818 Collell and Fauquet Brain activity and cognition both, thermodynamic-based brain models and information- theory framework (Anderson, 1996; Friston and Stephan, based models of cognition (Collell and Fauquet, 2014). For 2007). However, a connection between information theory instance, it has yet to be studied whether the equations of both and thermodynamics has not been formalized in neuroscience modelizations are consistent. In this sense, if a thermodynamic- yet (Del Castillo and Vera-Cruz, 2011; Collell and Fauquet, based model predicts a change of the system in a certain 2014). This article aims at further elaborating the idea that we direction by considering energetic measures, an information- introduced in a previous paper (Collell and Fauquet, 2014), based model should predict a change in the same direction if namely to develop a suitable framework to connect information- these thermodynamic measures were translated into information. based models of cognition and thermodynamic models of the In order to briefly introduce the relationship between brain. In this respect, the main contribution of this work information and physics, let us suggest the following thought is studying this relationship from a new perspective, that is, experiment proposed in 1867 which is known as Maxwell’s from the classical connections between information theory and demon paradox. In our opinion, this paradox is not only useful thermodynamics (see Figure 1). Ultimately, this paper aims at to understand the relationship between thermodynamics and expanding the formal connection between physical brain activity information theory, but also to gain insight on how mind and cognition. computations are linked to energy and information. In short, This paper is structured as follows. In the following section, consider a container divided in two parts, A and B, both we analyze how thermodynamics is linked to brain activity and filled with the same gas at equal temperatures. A tiny demon we present some relevant physically-principled models. Next, we is guarding a trapdoor between A and B and when a faster- present Friston’s information-based model and then we propose a than-average molecule is moving toward A, he allows it to list of different means to obtain information measures from brain pass by briefly opening the trap and closing it immediately. and cognitive activity. In the next section, we discuss the classical Similarly, he allows slower-than-average molecules to pass to connections between information theory and thermodynamics B. After a while doing this task, the temperature, i.e., average and afterwards we analyze how these connections should be molecular speed, will be higher in A than in B. This implies applied within the brain context. Then, we establish theoretical that the entropy (disorder, for now) of the system would have bridges between the previously described brain and cognitive decreased, leading to an apparent violation of the second law models by applying the classical links between information of thermodynamics, which states that entropy can only increase theory and thermodynamics. Next, we suggest how the question for an isolated system. Afterwards, this temperature difference of spontaneity—applied to brain and cognitive activity—can be can be used to produce work (Feynman et al., 1998). Maxwell’s addressed from the framework proposed here. Finally, in the demon paradox was not considered completely solved until more discussion, we summarize and analyze the contributions of our than a century after its proposal. This solution will be disclosed approach and we propose future lines of research. and briefly commented on afterwards. Remarkably, even without ever having seen any formalization of the concepts of information and physical entropy before, one can intuitively realize from this Thermodynamics and Brain Activity thought experiment that “knowledge” about the system (cold vs. hot molecule) can somehow be translated into useful energy. The Overview of Thermodynamics of Open converse, namely the fact that energy can be transformed into Dissipative Systems information, was perhaps clear and widely accepted from the A core concept in thermodynamics is entropy. It is often regarded beginning since in our digital age it does not come as a surprise asthedegreeofdisorderofthesystem,butitequalstotheamount for anyone that computers consume energy in order to encode or of energy dissipated in form of molecular vibration that cannot erase data. be used to produce work, according to its precise definition Several brain and cognitive models have been proposed so far (Feynman et al., 1965). For example, recalling Maxwell’s demon from the thermodynamic viewpoint (Kirkaldy, 1965; La Cerra, context, there is the same amount of energy in the initial as in the 2003; Varpula et al., 2013) as well as from the information final situation since there is the same total amount of molecular FIGURE 1 | Connection between brain activity (left) and cognitive models (right) by means of the classical links between thermodynamics and information theory (middle). Frontiers in Psychology | www.frontiersin.org 2 June 2015 | Volume 6 | Article 818 Collell and Fauquet Brain activity and cognition vibration, but in the first scenario it was not possible to use this can be described by the Helmholtz free energy FH formula energy to produce work. The first formal definition of physical (Prigogine,
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