In physics, especially in statistical physics, quantum physics or its derivatives, you can find an extremely fascinating word, the distribution of a system. Boltzmann was among the first to notice the great importance of distributions, with his famous statistical distribution in a microscopic system of large numbers of particles, then Planck was able to find the missing relationship in his black body work with the use of distributions and the combinations, thus quantizing the energy that a particle and a photon can acquire.
What do the distributions tell us?
Since at time t, the system will be spatially distributed in some way. But not only that, the system will have some physical information that will be of interest to us. Energy is an example, if given a distribution of three electrons, how does energy behave in this system?
In the case just mentioned, we are measuring the energy of the system without external interaction with another body or system, the energy in this case must be conserved. Additionally, and as is well known, it does not matter how the energy is expressed within the system, it does not matter if it is kinetic, potential or electromagnetic energy. Its sum must be preserved regardless of its configuration. Extrapolating the idea, we can obtain any relevant information from a multi-body system, only knowing its distribution with respect to the information we want to know, here comes the combinatorics. If we measure the system at different moments in time, the distribution between the information and the bodies would change, being then clearly dependent on time. If the transformation from a distribution 1 to another distribution 2, given a time interval, does not change its measurable macroscopic information, then the system conserves that physical information, it is not dependent on time. The physical information is a generalization for the eigenvalue of an operator, being then the observable of its corresponding operator.
Now I am going to present a simple idea in great depth of interacting systems. We know that in order to modify the motion constants of a system, it must be exposed to a potential or interaction of another system. We are going to consider a microscopic system which is irradiated by information from another but macroscopic system (in this way so that the macroscopic system does not suffer considerable changes in the system).
Idea:
If we change the distribution of a compound system, it changes the way it receives and reflects physical information (energy for example). So, this changes since this received physical information has to be a part assimilated by the system distribution, thus changing its internal information and reconfiguring it with new possible distributions. Possible distributions since what changes at the end of the process is the possibility (probability) of the system to acquire new states that were not allowed before. In tau time, there will be an imbalance in the system due to excess information, it will then be a process where a part is absorbed and another part reflected, the system has become asymmetric and unbalanced.
An unbalanced system always tends to balance, so there can be three types:
Internal balance with new configurations acquired (states) by the new information.
Balance by total reflection of the information, something like a super mirror. In this case the system tends to return to its initial state (or states).
Balance for new internal information and for reflected information. Now the reflected information will not be equal to the one incident at the beginning, there will be a modification which is proportional to the distribution of the microscopic system.
Conclusion:
The idea is a way of simplifying the way in which new information can change an initial system, therefore changing its total energy and possible states that it can acquire in a distribution. The modification mentioned in the last type of system can be proportional to the geometry of the system, spatial combinations, or even something more abstract than that, such as the density of information or states that the system has before the incidence of information by another. system. The information that we measure from a system is then dependent on the measurement (incident information) and the system (distribution).
In the disequilibrium process, the continuity equation holds. Taking the information density as density and the information change propagation vector as the continuity vector. It is true because at that time there is a change in the density of information (also density of states). And what could a physicist measure without changing a system? I leave this question to the reader.
"The only constant in life is change." (Buddha, philosopher).
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