They are different, but fortunately they are related by the famous formula incorrectly credited to Ludwig Boltzmann, namely, S = k log W, where W is the number of microphysical configurations or orders compatible with the macrostate
characterized by the entropy S and other macroproperties.
where [S.sub.B] ([GAMMA]) is the system entropy in the macrostate
[GAMMA], [kappa] is Boltzmann's constant and [W.sub.[GAMMA]] is proportional to the macrostate
This is consistent with the usual understanding of entropy as hidden information; indeed, the true information about the microstates is not accessible (only the macrostate
), and this is what entropy stands for.
Furthermore, as stated earlier, each macrostate
[theta] is in a one-to-one correspondence with the probability distribution p(x | [theta]).
State vertexes in the same group can be aggregated as a macrostate
, and transitions between macrostates
are formed as macroactions (i.e., options).
This formulation, after the integration over the variable x, produces a result for the macrostate
probabilities in the system.
Any Entropie Field is a collection of Microstates (assembled into a Causal Macrostate
or Phase as part of a Causal Process cycle) causally generated one from another as an Effect of the Causal Couple Temperature / Information variation.
To simplify the analysis of the Markov chain [[xi].sub.t], t [greater than or equal to] 0, let us enumerate the states of this process in the direct lexicographic order of the components r, n, w, v, m, and refer to the set of the states of the Markov chain having values (i, r) of the first two components of the Markov chain as the macrostate
Shannon's concept of information, based on Boltzmann's equation about the relationship between entropy, microstate, and macrostate
, does not specify sequence subunits.
It should be noted that each microstate belongs to exactly one macro-state; each macrostate
has exactly one entry micro-state and one exit microstate and the two may overlap.
The aim of the work is the analysis of dimensional boundary between the nano-and macrostate
and mathematical description of the nanoparticle term.