# DISCOVERY OF “QUANTUM NUMBERS” IN THE CARDIOPULMONARY INTERACTION STUDIED IN THERMODYNAMICS WITH FINITE SPEED

**Autor/autori**: Stoian PETRESCU, Valeria PETRESCU , Monica COSTEA, Liliana TIMOFAN,
Silvia DANES, Georgeta BOTEZ

**Abstract**: The paper proposes an extension of Thermodynamics with Finite Speed (TFS) to Biological Systems, with Cardio-Pulmonary System study as the first objective. It is an extremely important system in the functioning of any blood beings (including humans). For stationary states, three fundamental state parameters were introduced: Heart frequency, Fi, Lung frequency, Fp, and their ratio, Rf, in order to describe the self-organized interaction between them. With these new parameters of state one could also describe Processes “between” stationary states, as it was already done for several Thermal Machines by using TVF and instantaneous average parameters such as instantaneous average internal energy, Umi, instantaneous average entropy, Smi. Since the heart and lungs frequencies are proportional to the energy consumed by each of them, these two quantities „are similar” to Umi. Their ratio, Rf, is also proportional to the ratio of these energies and will characterize the interaction of the two subsystems. Using these new parameters, an analytical formula linking the two properties was sought, by studying the experimental behavior of Rf in time. Numerous experiments have led to a very interesting and important conclusion, stating that Rf is a function of a “quantum number” N (integer). Based on the experimental findings, a new formula correlating the Speed of Lungs, Fp, with the Speed of Heart, Fi, in their continue interaction was “invented”. This formula is absolutely essential for TFS extension to Biological Systems. It will alow to find analytical expressions for Power and Efficiency of Heart and Lungs as a function of a single speed, Fi, as it was previously done for a wide range of Thermal Machines (as a function of the piston speed that is the main parameter in TFS). Designers can now use these analytical formulas for more efficient and optimized design of artificial hearts and lungs customized for each patient.

**Keywords**: “Quantum Numbers” in the Heart-Lungs Interaction, Thermodynamics with Finite Speed, Cardio-Respiratory System, Self-organization of Heart-Lung Interaction, Quantum Formula of the correlation between Heart and Lung Frequencies, Stationary States and Processes with quantum jump in the Cardio-Respiratory System