in the [1]The authors represent the *Causal path entropy* as follows:

For every open thermodynamic system like a biological organism we can do this

Treating phase space paths that the system takes over a period of time

$[0,tau]$ as microstates and divide them into macrostats

$ {X_i } _ {i in I} $ using the equivalence relationship:begin {equation} x (t) sim x & # 39; (t) iff x (0) = x & # 39; (0) end {equation}

As a result, we can identify every macrostat $ X_i $ with a gift

system state $ x (0) $,We can then define the causal path entropy $ S_c $ from a makrostat $ X_i $

assigned to the current system state $ x (0) $ as path integral:begin {equation} S_c (X_i, tau) = – k_B int_ {x (t)} P (x (t) | x (0)) ln P (x (t) | x (0)) Dx (t) end {equation}

from where $ k_B $ is the Boltzmann constant.

Well, the authors of [1] I claim that this is a new kind of entropy, and this is a point that I would like to clarify because it looks like this is simply a conditional Boltzmann entropy.

Actually on the second page of [2] C. Villani introduces Boltzmann entropy using time-dependent density $ f $ on particles in phase space $ (x, v) in omega times mathbb {R} _v ^ 3 $:

begin {equation}

S (f) = – int _ { Omega times mathbb {R} _v ^ 3} f (x, v) ln f (x, v) dxdv

end {equation}

and we can analyze the dependence of the development of $ S $ under special initial conditions $ p (0) = (x_0, v_0) $ by the definition of:

begin {equation}

S (f | p (0)) = – int _ { Omega times mathbb {R} _v ^ 3} f (p (t) | p (0)) ln f (p (t) | p (0)) dp

end {equation}

from where $ p in omega times mathbb {R} _v ^ 3 $

I am relatively new to statistical mechanics, but I would be very surprised if it did not occur to him to analyze $ S (f | p_0) $, Is the causal path entropy actually conceptually new?

**Note:** Although I mention the Boltzmann entropy here, I have to say that the authors of [1] do not count on Boltzmann for their ideas. Meanwhile, in a relatively recent TED talk, Wissner-Gross claims that & # 39; E = mc ^ 2 & # 39; to have discovered for the intelligence.

references:

- Gross, A. Wissner. (2013) Causal entropic forces. Physical overview letters.
- Villani (2007) H-Theorem and beyond: Boltzmann's entropy in today

Mathematics.