Hi FISers, I think information and energy are inseparable in reality. Hence to understand what information is, it may be helpful to understand what energy (and the associated concept of motion) is. In this spirit, I am forwarding the following email that I wrote motivated by the lecture given by Dr. Grossberg this afternoon at the 119th Statistical Mechanics Conference. In Table 1 in the email, I divided particle motions studied in physics and biology into three classes -- (i) random, (ii) passive, and (iii) active, and identified the field of specialization wherein these motions are studied as (i) statistical mechanics, (ii) stochastic mechanics, and (iii) info-statistical mechanics. The last term was coined by me in 2012 in [1]. I will be presenting a short talk (5 minutes) on Info-statistical mechanics on Wednesday, May 9, at the above meeting. The abstract of the short talk is given below:

Short talk to be presented at the 119th Statistical Mechanics Conference, Rutgers University, Piscataway, N.J., May 6-9, 2018). Planckian Information may be to Info-Statistical Mechanics what Boltzmann Entropy is to Statistical Mechanics. Sungchul Ji, Department of Pharmacology and Toxicology, Ernest Mario School of Pharmacy, Rutgers University, Piscataway, N.J. 08854 Traditionally, the dynamics of any N-particle systems in statistical mechanics is completely described in terms of the 6-dimensional phase space consisting of the 3N positional coordinates and 3N momenta, where N is the number of particles in the system [1]. Unlike the particles dealt with in statistical mechanics which are featureless and shapeless, the particles in biology have characteristic shapes and internal structures that determine their biological properties. The particles in physics are completely described in terms of energy and matter in the phase space but the description of the particles in living systems require not only the energy and matter of the particle but also their genetic information, consistent with the information-energy complementarity (or gnergy) postulate discussed in [2, Section 2.3.2]. Thus, it seems necessary to expand the dimensionality of the traditional phase space to accommodate the information dimension, which includes the three coordinates encoding the amount (in bits), meaning (e.g., recognizability), and value (e.g., practical effects) of information [2, Section 4.3]. Similar views were expressed by Bellomo et al. [3] and Mamontov et al. [4]. The expanded “phase space” would comprise the 6N phase space of traditional statistical mechanics plus the 3N information space entailed by molecular biology. The new space (to be called the “gnergy space”) composed of these two subspaces would have 9N dimensions as indicated in Eq. (1). This equation also makes contact with the concepts of synchronic and diachronic informations discussed in [2, Section 4.5]. It was suggested therein that the traditional 6N-dimensional phase space deals with the synchronic information and hence was referred to as the Synchronic Space while the 3N-dimensional information space is concerned with the consequences of history and evolution encoded in each particle and thus was referred to as the Diachronic Space. The resulting space was called the gnergy space (since it encodes not only energy but also information). Gnergy Space = 6N-D Phase Space + 3N-D Information Space (1) (Synchronic Space) (Diachronic Space) The study of both energy and information was defined as “info-statistical mechanics” in 2012 [2, pp. 102-106, 297-301]. The Planckian information of the second kind, IPS, [5] was defined as the negative of the binary logarithm of the skewness of the long-tailed histogram that fits the Planckian Distribution Equation (PDE) [6]. In Table 1, the Planckian information is compared to the Boltzmann entropy in the context of the complexity theory of Weaver [8]. The inseparable relation between energy and information that underlies “info-statistical mechanics” may be expressed by the following aphorism: “Information without energy is useless; Energy without information is valueless.” Table 1. A comparison between Planckian Information (of the second kind) and Boltzmann entropy. Adopted from [6, Table 8.3]. Order Disorder IPS = - log2 [(µ - mode)/σ] (2008-2018) S = k log W (1872-75) Planckian Information Boltzmann entropy [7] Organized Complexity [8] Disorganized Complexity [8] Info-Statistical Mechanics [2, pp. 102-106] Statistical Mechanics [1] References: [1] Tolman, R. C. (1979). The Principles of Statistical Mechanics, Dover Publications, Inc., New York, pp. 42-46. [2] Ji, S. (2012) Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications. Springer, New York. [3] Bellomo, N., Bellouquid, A. and Harrero, M. A. (2007). From microscopic to macroscopic descriptions of multicellular systems and biological growing tissues. Comp. Math. Applications 53: 647-663. [4] Mamontov, E., Psiuk-Maksymowitcz, K. and Koptioug, A. (2006). Stochastic mechanics in the context of the properties of living systems. Math. Comp. Modeling 44(7-8): 595-607. [5] Ji, S. (2018). Mathematical (Quantitative) and Cell Linguistic (Qualitative) Evidence for Hypermetabolic Pathways as [SJ1]<file:///C:/Users/sji/Dropbox/SMC_2018/Ji_Spring_2018.docx#_msocom_1> Potential Drug Targets. J. Mol. Genet. Medicine (in press). [6] Ji, S. (2018). The Cell Language Theory: Connecting Mind and Matter. World Scientific Publishing, New Jersey. Chapter 8. [7] Boltzmann distribution law. https://en.wikipedia.org/wiki/Boltzmann_distribution. [8] Weaver, W. (1948) Science and Complexity. American Scientist 36:536-544. - - - - - - - - - - - - - -the Email to Dr. Grossberg --------------------- - - - --- - -- - - - - - - - - - - - - - ________________________________ Hi Dr. Grossberg, Thank you for your thought-provoking lecture (entitled "From Sisyphus to Boltzmann: an example of repulsive depletion interaction") this afternoon at the 119th Statistical Mechanics Conference at Rutgers. Your lecture prompted me to construct the following table based on my experience as a theoretical cell biologist over the last 4 decades as summarized in [1, 2]. According to Table 1, we can recognize three distinct kinds of particle motions in physics and biology that may be studied in 3 distinct fields of specialization, tentatively identified with (i) statistical mechanics, (ii) stochastic mechanics, and (iii) what I recently referred to as "info-statistical mechanics" [1,pp. 102-107; 2, pp. 371-374]. Table 1. The trichotomy of particle motions in physics and biology Particle Motions (Discipline) Random motion (1) (Statistical mechanics) Passive motion (2) (Stochastic mechanics ?) Active motion (3) (Info-statistical mechanics ?) [1, 2] Energy Source homogeneous thermal environment external (e.g., magnetic field) internal (e.g., chemical reactions) Physics dust particles in water at equilibrium dust particles in water in flow a piece of sodium metal in water at equilibrium Brownian motion e.g., Orenstein-Uhlenbeck process artificial molecular machines Biology dead bacteria in water at equilibrium live bacteria moving down a gradient live bacteria swimming against a gradient Brownian motion diffusion driven by gradient Chemotaxis driven by ATP hydroly * In your lecture today,. you referred to "active motions" of inanimate particles, which seems to correspond to "passive motions" in the above table, since the driving force for your particle motion is external to the particle. If you wish to preserve the term "active motion", it seems to me necessary to differentiate between the "externally driven active motion" and the "internally driven active motion". On the other hand, if we adopt the terms,"active" vs. "passive" particle motions, we have a precedence in biology where "active transport" (e.g., the Na/K pump) and "passive transport" (e.g., the Na/Ca exchange channel) are well known. In fact, the triadic classification of particle motions defined in Table 1 can be applied to ion movements across biomembranes with an equal force. If you have any questions or comments on the suggestions made in Table 1, I would appreciate hearing from you. All the best. Sung References: [1] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications. Springer, New York. [2] Ji, S. (2018). The Cell Language Theory: Connecting Mind and Matter. World Scientific Publishing, New Jersey. With all the best. Sung

_______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis