Content table
Quantum processing
Today, quantum algorithms are used to model and process the information of biosystems, especially in the decision-making process and understanding their behavior. In fact, since a living system is essentially open (an isolated system is a dead system), open quantum systems theory is the most powerful tool for modeling them. In other words, a biosystem is a black box that is processing quantum information [1]. Because the quantum representation of information is the distinguishing feature of all biological systems, from proteins, genomes and cells to the brain and ecological systems [2].
But why go to the quantum processing of biological information?
Because it allows the analysis of unresolved uncertainties. Mathematically, they are encoded as superpositions of states. The main advantage of such information processing is to save calculations. In fact, the biosystems that work in the quantum structure do not need to solve all the uncertainties and determine the probability distribution at each stage of processing the states. In this case, the state is not interpreted as a physical or chemical state, but as an informational state of the biosystem. This idea has also been applied to model the quantum representation of information processing by the brain [2].
In quantum models, stability of order in biological systems is the result of superposition-based information processing. To put it better, the goal of quantum algorithms is to process all ambiguities as quickly as possible without trying to resolve ambiguity or disorder. As a result, quantum processing, which plays the main role in the structure of logical operations, is considered the most appropriate option for examining biological data [3].
Quantum entropy
The author of reference [4] considers maintaining order as one of the main distinguishing features of biosystems and states entropy as a suitable quantitative measure for its measurement. In fact, the main message of the book [4] is that biosystems are not only subject to material or energy limitations imposed by the physical environment, but also to informational limitations imposed by the information environment. In fact, biosystems as open systems are constantly interacting with their physical-informational environment.
Therefore, entropy tends to increase in these systems, but biological structures are always trying to control it. Because according to reference [5], life is not possible without energy and matter, but life is not possible without information either. And if the entropy level is not controlled, we will face information loss.
In the meantime, one of the appropriate criteria for investigating the ambiguities and information level of a biological system is the quantum entropy parameter. Quantum entropy represents the uncertainty in the distribution of states of quantum information. This type of entropy is fundamentally different from classical entropy. Because in particular, it can violate the second law of thermodynamics and be preserved even for an isolated system. In other words, for open quantum systems, the problem of escaping the transition to disorder can be formalized by quantum Markov dynamics. But according to this theory, a biosystem by processing quantum information can maintain and even reduce its entropy in the process of information exchange with its environment, thus maintaining or even improving its order structure [2].
Logical quantum entropy is introduced as a direct measure of defining information in terms of distinctions, differences, discriminability and diversity. The logical entropy formula dates back to the early 20th century, but the current development comes from seeing this formula as a quantification of the information in a segment as the normalized number of distinctions or dits (ordered pairs of elements in different blocks). Just as the Laplace-Boule notion of probability, as the normalized number of elements in a subset, quantifies the logic of subsets, logical entropy, as the normalized number of distinctions in a segment, quantifies the logic of segments, hence the segment label. determines the relevant The logical entropy of a segment is, in fact, a measure of probability, the probability of obtaining segment distinctions in two independent samplings of the original set [6].
Apart from replacing the usual concept of Shannon’s entropy, the point is to show that Shannon’s entropy is a slightly different part of the same concept of information as differentiation. That is, the minimum average number of binary segments (bits) that must be concatenated to create the distinctions of a segment. In fact, there is a non-linear bit-to-bit conversion that converts all simple, common, conditional, and mutual logic entropy concepts into Shannon entropy formulas [6].
The foundations of classical and quantum logical information theory are built on the logic of partitions, which is cognate (in the classification-theoretic sense) to the usual Boolean logic of subsets [7]. Regarding the congruence between partitions and subsets, it should be noted that quantitatively, the network of partitions plays the role that the Boolean algebra of subsets plays for size or probability, to the point where some researchers have suggested that information theory should have started with sets. Not from possibilities [7].
(logical probability theory) / (Boolean of subset) = (logical information theory) / (logical of partitions)
A selection of logical quantum entropy mathematical relations
The concept of information began as a criterion for distinguishing from the distinction of sets. The information set of a section Ο={B_1,β¦.,B_I} on a limited reference set called U, where the set of distinctions is equal to dit:
dit(Ο)={(u,u^β ): β B_i,B_(i^β )βΟ,B_iβ B_(i^β ),uβB_i,u^ββB_(i^β )}
The normalized size of a set is equal to the logical probability of its occurrence, and the normalized size of the set πππ‘ of a partition is equal to the understanding of the information contained in that set. Therefore, the logical entropy of a partition like π is represented by β(π) and it is defined based on the size of its set πππ‘ with the symbol πππ‘πβπΓπ as follows [7]:
According to any probability measure, π:πβ[0,1] on π={π’1,β¦,π’π} where ππ=ππ’π for π=1,2,β¦,π, measures the product πΓπ :πΓπβ[0,1] for every binary relationship π βπΓπ is equal to:
πΓππ =π’π,π’πβπ ππ’πππ’π=π’π,π’πβπ ππππ
Logical entropy π in general is equal to measure the probability of the product of its set πππ‘ so that Prπ΅=π’βπ΅π(π’):
βπ=πΓππππ‘ π=π’π,π’πβπππ‘(π)ππππ=1βπ΅βπPrπ΅2
Proposing bioresonance device data analysis based on logical quantum entropy mathematical relationships
Bioresonance therapy is a medical treatment approach in which electromagnetic waves can be used to diagnose and treat human diseases. Based on this, in reference [8], a new non-invasive method for cancer diagnosis and treatment is proposed through the three-dimensional NLS bio-feedback system. In this article, the author believes that human cells, which are composed of molecules and atoms, have information, biological noise, biophysical noise and entropy with the theory of epic quantum logic. It also states that the human system is not a closed system, but an open system and continuously exchanges materials, energy and information with the environment. So, as it seems, we are again dealing with the analysis of a biosystem.
In this article, the theory of logical quantum entropy in biological systems is comprehensively discussed. The author believes that the concept of entropy can be properly used to analyze living organisms. Because a living organism is always exporting entropy to reduce its internal entropy level. In other words, from the point of view of thermodynamics, every organism should be defined as a non-equilibrium open system. A steady state exists when its internal parameters stabilize at the survival level. As a result, steady state stability can be maintained only as a result of intense exchange between the living system and its environment by energy, entropy, matter and information [8].
According to the laws of cybernetics, any system will work if there are two signals: input and output. In fact, we can know about the characteristics of processes inside the system while evaluating the input and output signals of the system [8]. The output of the NLS biofeedback device always contains two spectra; Two spectrums in a specific frequency range containing 9 frequencies. What the device declares the proximity to a disease based on, comparing two spectra belonging to the person being examined with all the two spectra in the device’s library.
What is intended in this research is to examine and determine the comparison criteria of the person being examined with the device library. One of the suggestions of the wave to matter team is the two-dimensional display of spectra in ordered pairs. In other words, the desired person should be shown using 9 ordered pairs in two-dimensional space and measured with 9 ordered pairs of other diseases. In this regard, several criteria such as Euclidean distance, the set of larger eigenvalues have been investigated in clustering algorithms such as decomposition into principal components, etc.
According to the explanations of the previous sections, as well as the idea in reference [7], any difference can be raised by the binary space, and also according to the speed of information processing by the human brain, our suggestion is to use the quantum algorithm. So that the spectra of each human’s body is considered as a random set and measured in the topological space with other diseases. One of the reasons that has made us more determined to implement this proposed idea is the indirect reference of many references related to the resonance biofeedback device to this measurement criterion.
References of theoretical foundations and modeling in bioresonance
[1]
I. &. K. A. Basieva, ” What is life?”: Open quantum systems approach., 2022
[2]
M. B. I. K. A. O. M. T. Y. &. Y. I. Asano, Quantum information biology: from information interpretation of quantum mechanics to applications in molecular biology and cognitive psychology, Foundations of Physics, 45, 2015
[3]
K. Svozil, Quantum logic, Springer Science & Business Media, 1998
[4]
L. &. S. D. Margulis, What is life?., Univ of California Press., 2000
[5]
H. A. Johnson, Information Theory in Biology after 18 Years: Information theory must be modified for the description of living things., Science, 168(3939), 1545-1550, 1970
[6]
D. Ellerman, Introduction to logical entropy and its relationship to Shannon entropy, University of Ljubljana, Slovenia, 2021
[7]
D. Ellerman, Logical entropy: Introduction to classical and quantum logical information theory, Entropy, 20(9), 679, 2018
[8]