Stoian PETRESCU 1, Bogdan BORCILA 1, *Monica COSTEA 1, Romi BOLOHAN 2, Valeria PETRESCU 1, Michel FEIDT 3, Georgeta BOTEZ 4

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1 ABOUT THE ORIGIN OF STATIONARY STATES AND PROCESSES WITH OR WITHOUT QUANTUM JUMP IN THE CARDIO- PULMONARY SYSTEM, DESCRIBED IN QUANTUM BIOLOGICAL THERMODINAMICS WITH FINITE SPEED Stoian PETRESCU 1, Bogdan BORCILA 1, *Monica COSTEA 1, Romi BOLOHAN 2, Valeria PETRESCU 1, Michel FEIDT 3, Georgeta BOTEZ 4 1 University POLITEHNICA of Bucharest, Department of Thermotechnics, Engines, Thermal and Refrigerating Equipment, 313 Splaiul Independentei, Bucharest, Romania 2 Emergency Center for Cardiovascular Diseases Dr. Constantin Zamfir, Clinic of Cardiology, Electrophysiology and Arrythmology, 134 Calea Plevnei, Bucharest, Romania 3 Université de Lorraine, L.E.M.T.A., U.R.A. C.N.R.S. 7563, 2, avenue de la Forêt de Haye TSA 60604, Vandoeuvre CEDEX, France 4 Sindan Pharma, 11 Bd. Ion Mihalache, Bucharest, Romania * Corresponding author: liana5802@yahoo.fr Abstract Considering the Cardio-Pulmonary System as a group of two biological machines: a liquid pump with valves (the Heart) and two air compressors (the Lungs), similarities with a two pistons machine, as Stirling Machine were found. Thus, Thermodynamics with Finite Speed (TFS) for Thermal Machines was found suitable to be extended to Biological Systems study. Based on the experimental discovery of Stationary States and Processes between them in the Cardio Pulmonary System, we built a new branch of Thermodynamics of Irreversible Processes for Biological Systems, we called Quantum Biological Thermodynamics with Finite Speed. This new theory is based on an interesting and important experimental discovery, namely the correlation of the Heart Frequency with the Lungs Frequency through an integer number N. We called it the Quantum Number of the Stationary State. This paper aims to explain the origin and significance of this correlation, as well as of the quantum number N. It also presents the four diagrams we have invented in order to illustrate the interaction of these two biological systems. They are able to show the Stationary States distribution over a day and in connection with different positions or activities of a person. Also, they are helpful in explaining the origin of Processes with or without Quantum Jump between Stationary States in the Cardio- Pulmonary System. Keywords: Hearth and Lung Frequencies, Processes with Quantum Jump in Cardio- Pulmonary System, Quantum Biological Thermodynamics with Finite Speed, Stationary States in Cardio-Pulmonary System. Introduction We consider the Cardio-Pulmonary System as a group of two biological machines: a liquid pump with valves (the Heart) and two air compressors (the Lungs). After we invented Thermodynamics with Finite Speed (TFS) [1-12] and validated it for 15 Stirling Motors [9-11] we have discovered several similarities between Cardio-Pulmonary System and Stirling Machines. The first similarity is the fact that these two Systems (an engineering System- Stirling Machine, and a Biological System-Cardio-Pulmonary System) have two pistons. A

2 second similarity is the fact that between the Frequency of the two pistons oscillating motion there is a very well organized correlation from the point of view of Frequency and phase of oscillations. Because of these two extremely important similarities, five years ago we started to believe that Thermodynamics with Finite Speed (TFS) for Thermal Machines is suitable to be extended to the study of an extremely important Biological Systems, namely the Cardio-Pulmonary System. Based on the experimental discovery of Stationary States and Processes between them in the Cardio Pulmonary System, we built a new branch of Thermodynamics of Irreversible Processes for Biological Systems, we called Quantum Biological Thermodynamics with Finite Speed (QBTFS) [13-24]. This new theory is based on an interesting and important experimental discovery, namely the correlation of the Heart Frequency F H with the Lungs Frequency F L, through an integer number N, called by us the Quantum Number of the Stationary State. This paper aims to explain the origin and significance of this correlation, as well as of the quantum number N. It also presents the four diagrams we have invented in order to illustrate the interaction of these two biological subsystems. They are able to show the Stationary States distribution over a day and in connection with different positions or activities of a person. Also, they are helpful in explaining the origin of Processes with or without Quantum Jump between Stationary States in the Cardio- Pulmonary System [13-24]. 1 Discovery of the formula correlating Heart Frequency with Lung Frequency After doing thousands measurements of F H and F L for more than 180 people in Stationary States we have discovered that there is a very simple quantized formula which correlates the two frequencies in healthy persons: FH N Rf = = 2 + (1) FL 4 where: F H = Heart Frequency, F L = Lungs Frequency, N = Phase quantum number (which established the fact that in the case of healthy person there is a very organized correlation between the two oscillations from the point of view of oscillation phase). This is very similar with the fact that in the two pistons oscillation of a Stirling Engine, only for a phase difference of 90, the engine has the maximum efficiency. In a similar way, the Cardio-Pulmonary system operates efficiently only if a certain order is established regarding the Phase of oscillation in all Stationary States. The explanation of this self-organizing of the interaction between the two Pistons of the Cardio-Pulmonary Systems comes from the entanglement between the two oscillators, observed in many natural systems in Synergetics [25]. It has been discovered and demonstrated in Synergetics (new Science invented by H. Hacken [25]) that between two oscillators (of any origin: mechanical, electrical, magnetic, biologic, light-in lasers) in a self-organizing way an order of interaction is established, in such a way that the ratio of the frequency is correlated with a selforganization of the phase difference. In the case of the system we have studied (Cardio- Pulmonary System), the parameter which characterizes this self-ordering of oscillations, form the point of view of Phase is exactly the Phase quantum number N. This parameter of state, together with F H and F L, became the 3 parameters of Stationary States in the Cardio- Pulmonary System, similarly with the 3 parameters of state of Classical Reversible Thermodynamics, where p, V, and T, are the 3 parameters of equilibrium states of Thermodynamic Systems. Based on this similarity we have established the equations of Processes with or without Quantum Jump between Stationary States, in the Cardio - Pulmonary System for a healthy person. For persons with some heart problems, the stationary states cannot be achieved, and illness like atrial fibrillation or ventricular fibrillation can appear.

3 2 Four Diagrams describing the Stationary States and Processes with or without Quantum Jump in Cardio-Pulmonary System Based on the experimental measurements and with the help of formula (1) we have built four diagrams describing the Stationary States and Processes between Stationary States in healthy people. They are illustrated hereafter for a person (SP) aged 78 years and a younger one (BB) of 29 years. Figure 1 : Diagrams: F H = f(f L ) and F L = f(f H ) for SP (left) and BB (right) The analysis of the diagrams in Fig. 1 shows the distribution of stationary states corresponding to different positions (standing, sitting on a chair, lying in bed) during the experiments and the transition (process) between them, allowing the comparison of the frequency variation domain for the two persons. Many of the process lines from these diagrams of SP are parallel. All those processes have the same slope (ΔF L /ΔF H, ΔN/ΔF H, ΔF H /ΔF L, ΔN/ΔF L ), these can be characterized as iso-slope processes: - Iso-Rhythm (F L = constant): 4-5; 15-16, 18-19; - Iso-Quantum Number (N = constant): 9-10; 10-11; 16-17; 20-21; - Iso-Pulse (F H constant): 2-2, 3-3, 4-4, 5-5, 5-6. In the case of BB we have the following iso-slope processes: - Iso-Rhythm (F L = constant): 4-5, 10-11, 16-17; - Iso-Pulse (F H constant):

4 For person BB, fewer processes are iso-processes, most of them being polytropic processes. Their same slope shows in fact that for these processes the ratio between the variation of the corresponding stationary state parameters is the same. Figure 2 : Diagrams: R f and N = f(f L ), R f and N = f(f H ) for SP (left) and BB(right) In Fig. 2 the diagrams R f = f(f H ) and R f = f(f L ) allow characterization of the interaction state between the Heart-Lungs oscillating subsystems. They indicate that the cardio-pulmonary system of the two persons functions within normal limits, namely they reach slightly stationary states, namely integer values for N (on the right side ordinate), the quantum number. This gives validity to (1), the quantified Heart-Lungs interaction formula. Also, the iso-quantum processes can be easily identified on these diagrams (2 for SP and none for BB). The comparative analysis of the SP and BB diagrams shows how different they are in terms of Heart-Lungs interaction. Diagrams built for different people give them important information that characterizes the optimal functioning of the Cardio-Pulmonary System of each of them. Conclusions and Perspectives The paper presents the correlation of the Heart Frequency with the Lungs Frequency through an integer number named Quantum Number of the Stationary State. The origin and significance of this correlation and of the quantum number are explained based on the

5 similarities between the Stirling Machine and the Cardio-Pulmonary system. Thus, both of them have two pistons oscillating in a very well organized correlation of Frequency and Phase. Also, it was shown that this self-organized interaction between the two pistons of the Cardio-Pulmonary Systems comes from the entanglement between the two oscillators, that has been observed in many natural systems. The four diagrams we have invented in order to illustrate the interaction of these two biological sub-systems are presented. They are able to show the Stationary States distribution over a day and in connection with different positions or activities of a person. Also, they are helpful in explaining the origin of Processes with or without Quantum Jump between Stationary States in the Cardio-Pulmonary System The Quantum Biological Thermodynamics with Finite Speed of the Cardio-Pulmonary System (QBTFSCPS) becomes a very important new tool, mainly due to the 4 diagrams from section 2, for studying the Heart-Lungs Interaction in healthy and ill persons (with cardiopulmonary problems). These sort of studies open the perspective to help teams of designer (doctors, physiologists, biologist, electronic and mechanical engineers ) for a better design of artificial hearts and pacemakers. One priority in this direction would be for any person (any age) to draw these 4 diagrams when she is still healthy. Thus, if that person will get a very serious heart illness in time, the data of the diagrams could be useful in producing an artificial personalized heart that suits her best. We believe that in the near future any person could get a personalized heart or a personalized pacemaker. They could be designed to fit a person or a group of people with similar behavior of this interaction. In a previous paper [20] presented in 2016 at COFRET Conference we have shown: How different we are from the point of view of Heart-Lung interaction. Based on that paper we conclude that personalized artificial hearts and personalized pacemakers should be designed and produced in the near future. Based on observation from this paper (section 1) and the previously published papers and books [1-25] we believe that there is a very important and feasible opportunity to try a Unification between Thermodynamics with Finite Speed [20],[23], Thermodynamics with Finite Physical Dimensions [26], Synergetics (The entanglement theory of oscillations) [25], and Bejan s Constructal Theory [27]. References [1] L. Stoicescu, S. Petrescu, The First Law of Thermodynamics for Processes with Finite Speed, in Closed Systems, Bulletin I.P.B., Bucharest, XXVI(5), , 1964 [2] S. Petrescu, Contribution to the study of thermodynamically non-equilibrium interactions and processes in thermal machines, Ph.D. Thesis, I.P.B., Bucharest, 1969 [3] L. Stoicescu, S. Petrescu, Thermodynamic Processes Developing with Constant Finite Speed, Bulletin I.P.B., Bucharest, XXVI(6), , 1964 [4] L. Stoicescu, S. Petrescu, Thermodynamic Processes with Variable Finite Speed, Bulletin of I.P.B., Bucharest, XXVII(1), 65-96, 1965 [5] L. Stoicescu, S. Petrescu, Thermodynamic Cycles with Finite Speed, Bulletin I.P.B., Bucharest, XXVII(2), 82-95, 1965 [6] L. Stoicescu, S. Petrescu, The Experimental Verification of the New Expression of the First Law for Thermodynamic Processes with Finite Speed, Bull. I.P.B., Bucharest, XXVII(2), , 1965 [7] S. Petrescu, R. Iordache, G. Stanescu, A. Dobrovicescu, The First Law of Thermodynamics for Closed Systems, Considering the Irreversibilities Generated by Friction Piston-Cylinder, the Throttling of the Working Medium and the Finite Speed of Mechanical Interaction, Proceedings of ECOS'92 Conference, Zaragoza, Spain, edited by A. Valero and G. Tsatsaronis, 33-39, 1992 [8] S. Petrescu, C. Harman, The Connection between the First and Second Law of Thermodynamics for Processes with Finite Speed. A Direct Method for Approaching and Optimization of Irreversible Processes, Journal of the Heat Transfer Society of Japan, 33(128), 60, 1994

6 [9] S. Petrescu, M. Costea, C. Harman, T. Florea, Application of the Direct Method to Irreversible Stirling Cycles with Finite Speed, International Journal of Energy Research, 26(7), , 2002 [10] S. Petrescu, Lectures on New Sources of Energy, Helsinki University of Technology, 1991 [11] S. Petrescu, M. Costea, et al., Development of Thermodynamics with Finite Speed and Direct Method, AGIR Publishing House, Bucharest, 2011 [12] S. Petrescu, M. Costea, M. Feidt, I. Ganea, N. Boriaru, Advanced Thermodynamics of Irreversible Processes with Finite Speed and Finite Dimensions, AGIR Publishing House, Bucharest, 2015 [13] S. Petrescu, M. Costea, L. Timofan, V. Petrescu, Means for qualitative and quantitative description of the Cardio-Pulmonary System Operation within Irreversible Thermodynamics with Finite Speed, ASTR Conference CD, Sibiu, Romania, 2014 [14] S. Petrescu, V. Petrescu, M. Costea, L. Timofan, S. Danes, G. Botez, Discovery of Quantum Numbers In the Cardio-Pulmonary Interaction Studied in Thermodynamics with Finite Speed, Proceedings of ASTR Conference CD, Sibiu, Romania, 2014 [15] I. Ganea, S.A. Petrescu, L. Timofan, S. Petrescu, M. Costea, A socio-economic regularity established based on an analogy with Thermodynamic Processes with Finite Speed - An Equation for Standard of Living, Proceedings of ASTR Conference CD, Sibiu, Romania, 2014 [16] S. Petrescu, M. Costea, A.S. Petrescu, V. Petrescu, From Thermodynamics with Finite Speed towards Biological Quantum Thermodynamics with Finite Speed, Proceedings of the National Conference of Thermodynamics NACOT 15 CD, Iasi, Romania, 2015 [17] S. Petrescu, M. Costea, V. Petrescu, R. Bolohan, N. Boriaru, A.S. Petrescu, B. Borcila, Stationary Quantum States in Cardio-Pulmonary System, Proceedings of ASTR Conference CD, Galati, Romania, 2015 [18] S. Petrescu, M. Costea, A.S. Petrescu, V. Petrescu, N. Boriaru, R. Bolohan, B. Borcila, Processes with Quantum Jumps in the Cardio-Pulmonary System, Proceedings of ASTR Conference CD, Galati, Romania, 2015 [19] S. Petrescu, V. Petrescu, R. Bolohan, B. Borcila, M. Costea, Quantum Biological Thermodynamics with Finite Speed of the cardio-respiratory system as a new extension of Thermodynamics with Finite Speed, COFRET 2016 June 29-30, Proceedings of COFRET 16 CD, Bucharest, Romania, 2016 [20] S. Petrescu, V. Petrescu, R. Bolohan, B. Borcila, M. Costea, S. Danes, M. Feidt, G. Botez, G. Huminic, A. Huminic, N. Boriaru, G. Popescu, N. Manitiu, N. Dumitrascu, E. Panaite, T. Lozonschi, A. Gheorghian, How different we are in terms of Heart-Lung interaction: discovery and description in Quantum Biological Thermodynamics with Finite Speed, COFRET 2016 June 29-30, Proceedings of COFRET 16 CD, Bucharest, Romania, 2016 [21] S. Petrescu, R. Bolohan, V. Petrescu, B. Borcila, M. Costea, Diagrams Describing Stationary States and Processes in Cardio- Pulmonary System, Proceedings of ASTR Conference CD, Targu-Mures, Romania, 2016 [22] S. Petrescu, B. Borcila, M. Costea, R. Bolohan, V. Petrescu, G. Botez, What is Quantum Biological Thermodynamics with Finite Speed of the Cardio-Pulmonary System: a discovery or an invention?, Proceedings of the Romanian Academy, Series A, Constructal Law &Second Law Conference, Romanian Academy, Bucharest, 2017 [23] S. Petrescu, B. Borcila, M. Costea, R. Bolohan, V. Petrescu, G. Botez, Fundamentals in quantum biological thermodynamics with finite speed of the cardio-pulmonary system explained in 5 diagrams describing a relaxation process, Proceedings of ASTR Conference CD, Constanta, Romania, 2017 [24] B. Borcila, S. Petrescu, M. Costea, R. Bolohan, V. Petrescu, G. Botez, Effect of flue on Stationary States and Processes in the Cardio-Pulmonary System described in Quantum Biological Thermodynamics with Finite Speed, ACME Conference, Iasi, Romania, 2018 [25] H. Haken, Advanced Synergetics, Instability Hierarchies of Self-Organizing Systems and Devices, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1983 [26] M. Feidt, Thermodynamique Optimale en Dimensions Physiques Finies, Lavoisier, Paris, 2013 [27] A. Bejan, J.P. Zane, Design in Nature. How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization, Doubleday, New York, 2012

WHAT IS QUANTUM BIOLOGICAL THERMODYNAMICS WITH FINITE SPEED OF THE CARDIO-PULMONARY SYSTEM: A DISCOVERY OR AN INVENTION?

THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Special Issue/2018, pp. 249 254 WHAT IS QUANTUM BIOLOGICAL THERMODYNAMICS WITH FINITE SPEED OF THE CARDIO-PULMONARY