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         
                                        (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].



IPS = - log2 [(µ - mode)/σ]


S = k log W


Planckian Information

Boltzmann entropy [7]

Organized Complexity [8]

Disorganized Complexity [8]

Info-Statistical Mechanics [2, pp. 102-106]

Statistical Mechanics [1]

   [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 
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.  

    [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

Random motion (1)
(Statistical mechanics)

Passive motion (2)
(Stochastic mechanics ?)

Active motion (3)
(Info-statistical mechanics ?)
[1, 2]

Energy Source

homogeneous thermal environment

(e.g., magnetic field)

(e.g., chemical reactions)


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


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.


   [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.


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