Research Article
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Year 2022, Volume: 25 Issue: 3, 47 - 53, 01.09.2022
https://doi.org/10.5541/ijot.1105040

Abstract

References

  • C. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., 27, 379-423, 1948.
  • C.E. Shannon, W. Weaver, The Mathematical Theory of Communication, v. 1, University of Illinois Press, Urbana, Illinois, 1-131, 1964.
  • M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
  • E.T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev., 106 (4), 620–630, 1957.
  • S. Zhang, J. Li. “A bound on expectation values and variances of quantum observables via Renyi entropy and Tsallis entropy,” Int. J. Quantum. Inf., 19, 2150019, 2021.
  • J. Acharya, I. Issa, N.V. Shende, A. B. Wagner. “Measuring Quantum Entropy,“ arXiv:1711.00814. 2017.
  • L. Brillouin, “Science and Information Theory,” Physics Today, 9(12), 39, 1956.
  • P. Facchi, G. Gramegna, A. Konderak. “Entropy of quantum states,” arXiv:2104.12611. 2021.
  • I. Bialynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics”, Comm. Math. Phys. 44, 129-132, 1975.
  • F. C. E. Lima, a. R. P. Moreira, c. A. S. Almeida, “Information and thermodynamic properties of a non-hermetian particle ensemble,“ arXiv:2101.04803. 2021.
  • F. C. E. Lima, a. R. P. Moreira, L.E.S. Machado, A. S. Almeida. “Statistical properties of linear Majorana fermions,” Int. J. Quant. Chem. 121, e26749, 2021.
  • F. C. E. Lima. “Quantum information entropies for a soliton at hyperbolic well,|” arXiv:2110.11195. 2021.
  • R.S. Carrillo, C.A. Gil-Barrera, G.H. Sun, et al, “Shannon entropies of asymmetric multiple quantum well systems with a constant total length,” Eur. Phys. J. Plus 136, 1060, 2021.
  • R. Khordad, A. Ghanbari, A. Ghaffaripour. “Effect of confining potential on information entropy measures in hydrogen atom: extensive and non-extensive entropy,” Indian J. Phys, 94 (12), 2020.
  • S. Martiniani, P.M. Chaikin, D. Levine, “Quantifying hidden order out of equilibrium,” Phys. Rev. X 9, 011031, 2019.
  • O. Bahadır, H. Türkmençalıkoğlu, "Bilgi Kuramında Shannon Entropisi ve Uygulamaları," Eur. J. Sci. Tech., Special Issue 32, pp. 491-497, 2021.
  • K.E. Drexler, Nanosystems: Molecular machinery, Manufacturing, and computation, 1st Ed. Wiley, Hoboken, 576, 1992.
  • R. Nalewajski, “On entropy/information continuity in molecular electronic states,” Mol. Phys. 114 (1), 1225-1235, 2016.
  • M. Fannes, “Continuity property of the entropy density for spin lattice systems,” Commun. Math. Phys. 31 (4), 291–294, 1973.
  • KMR Audenaert, “A sharp continuity estimate for the von Neumann entropy,” J. Phys. A Math. Theor. 40 (28) 8127-8137, 2007.
  • T.R. Gingrich, J.M. Horowitz, N. Perunov at al, “Dissipation Bounds All Steady-State Current Fluctuations,” Phys. Rev. Lett. 116 (12), 120601, 2016.
  • P. Pietzonka P, A. Barato, U. Seifert, “Universal bounds on current fluctuations,” Phys. Rev., E 93, 052145, 2016.
  • A. Moldavanov, “Theoretical Aspects of Radiative Energy Transport for Nanoscale System: Thermodynamic Uncertainty,” J. Comput. Theor. Trans, 50(3), 236-248, 2021.
  • N.W. Tschoegl, Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, 2000.
  • R. G. Lerner, G.L. Trigg, Encyclopaedia of Physics 3nd ed. Wiley-VCH Verlag, Weinheim, 1994.
  • L.S. Grant, W.R. Phillips, Electromagnetism, 2nd ed., Wiley. Manchester Physics Series, Hoboken, 2008.
  • R.A. Serway, J.W. Jewett, V. Peroomian, Physics for scientists and engineers with modern physics. 9th ed. Pacific Grove: Brooks Cole, 2014.
  • A. Moldavanov. “Energy Infrastructure of Evolution for System with Infinite Number of Links with Environment,” BioSystems, 213, 104607, 2022.
  • A.V. Moldavanov, “Analytical and Numerical Model for Evolution of Minimal Cell with Infinite Number of Energy Links,”: Proceedings Mathematical biology and bioinformatics, Pushino, Russia, 8, article # e16. doi: 10.17537 /icmbb20.15, 2020.
  • A. Moldavanov. “Randomized Continuity Equation Model of Energy Transport in Open System,” in AMSM 2017: Proceedings of the 2017 2nd International Conference on Applied Mathematics, Simulation and Modelling, 258 – 265, 2017.
  • D. J. C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, Cambridge, 2003.
  • J.W. Gibbs, Elementary Principles in Statistical Mechanics. New York: Dover Publications, 1960.
  • L. Benguigui, “The different paths to entropy,” arXiv.org Solid State Institute and Physics department Technion Israel Institute of Technology 32000 Haifa. Israel 1-32, 2012.
  • C. Marsh, “Introduction to Continuous Entropy,” Department of Computer Science, Princeton University.
  • B.P. Levin, Theoretical basics of statistical radio engineering. 3rd revised ed. Radio and communication, Мoscow, 1989.
  • R. Swenson, “Emergent attractors and the law of maximum entropy production: Foundations to a theory of general evolution,” Syst. Res. 6(3), 187–197, 1989.
  • J. Uffink, J. van Lith. “Thermodynamic uncertainty relations,” Found. Phys. 29 (5), 655-692, 1999.
  • J.S. Hsieh, Principles of Thermodynamics. Washington, D.C.: Scripta Book Company, 1975.
  • A.E. Shalyt-Margolin, A. Ya. Tregubovich. “Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics,” Mod. Phys. Lett. A. 19(1), 71-81, 2004.
  • G. Wilk, Z. Włodarczyk. “Application of nonextensive statistics to particle and nuclear physics,” Phys. A: Stat. Mech. Appl. 305 (1-2), 227-233. 2002.
  • J. Lindhard, Complementarity’ between energy and temperature, in The Lesson of Quantum Theory. edited by de Boer J, Dal E, Ulfbeck O., 99-112, North-Holland, Amsterdam, 1986.
  • A. Faigon, “Uncertainty and Information in Classical Mechanics Formulation. Common Ground for Thermodynamics and Quantum Mechanics,” https://arxiv.org/abs/quant-ph/0311153, 2007.
  • J.M. Horowitz, T.R. Gingrich, ”Thermodynamic uncertainty relations constrain non-equilibrium fluctuations,” Nat. Phys. 16, 15–20, 2020.

Entropy of Open System with Infinite Number of Conserved Links

Year 2022, Volume: 25 Issue: 3, 47 - 53, 01.09.2022
https://doi.org/10.5541/ijot.1105040

Abstract

Energy budget of open system is a critical aspect of its existence. Traditionally, at applying of energy continuity equation (ECE) for description of a system, ECE is considered as a declaration of local balance in the mathematical (infinitesimal) vicinity for the only point of interest and as such it does not contribute to entropy. In this paper, we consider transformation of ECE to account the effects in the physical (finite) vicinity with infinite number of energy links with environment. We define parameters of appropriate phase space and calculate Shannon’s, differential, and thermodynamic entropy. Shannon’s and differential entropies look sufficiently close while thermodynamic entropy demonstrates close character of variation in its functionality being different in its mathematical form. Physical applications to confirm contribution of a new concept to the real-world processes are also discussed.

References

  • C. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., 27, 379-423, 1948.
  • C.E. Shannon, W. Weaver, The Mathematical Theory of Communication, v. 1, University of Illinois Press, Urbana, Illinois, 1-131, 1964.
  • M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
  • E.T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev., 106 (4), 620–630, 1957.
  • S. Zhang, J. Li. “A bound on expectation values and variances of quantum observables via Renyi entropy and Tsallis entropy,” Int. J. Quantum. Inf., 19, 2150019, 2021.
  • J. Acharya, I. Issa, N.V. Shende, A. B. Wagner. “Measuring Quantum Entropy,“ arXiv:1711.00814. 2017.
  • L. Brillouin, “Science and Information Theory,” Physics Today, 9(12), 39, 1956.
  • P. Facchi, G. Gramegna, A. Konderak. “Entropy of quantum states,” arXiv:2104.12611. 2021.
  • I. Bialynicki-Birula and J. Mycielski, “Uncertainty relations for information entropy in wave mechanics”, Comm. Math. Phys. 44, 129-132, 1975.
  • F. C. E. Lima, a. R. P. Moreira, c. A. S. Almeida, “Information and thermodynamic properties of a non-hermetian particle ensemble,“ arXiv:2101.04803. 2021.
  • F. C. E. Lima, a. R. P. Moreira, L.E.S. Machado, A. S. Almeida. “Statistical properties of linear Majorana fermions,” Int. J. Quant. Chem. 121, e26749, 2021.
  • F. C. E. Lima. “Quantum information entropies for a soliton at hyperbolic well,|” arXiv:2110.11195. 2021.
  • R.S. Carrillo, C.A. Gil-Barrera, G.H. Sun, et al, “Shannon entropies of asymmetric multiple quantum well systems with a constant total length,” Eur. Phys. J. Plus 136, 1060, 2021.
  • R. Khordad, A. Ghanbari, A. Ghaffaripour. “Effect of confining potential on information entropy measures in hydrogen atom: extensive and non-extensive entropy,” Indian J. Phys, 94 (12), 2020.
  • S. Martiniani, P.M. Chaikin, D. Levine, “Quantifying hidden order out of equilibrium,” Phys. Rev. X 9, 011031, 2019.
  • O. Bahadır, H. Türkmençalıkoğlu, "Bilgi Kuramında Shannon Entropisi ve Uygulamaları," Eur. J. Sci. Tech., Special Issue 32, pp. 491-497, 2021.
  • K.E. Drexler, Nanosystems: Molecular machinery, Manufacturing, and computation, 1st Ed. Wiley, Hoboken, 576, 1992.
  • R. Nalewajski, “On entropy/information continuity in molecular electronic states,” Mol. Phys. 114 (1), 1225-1235, 2016.
  • M. Fannes, “Continuity property of the entropy density for spin lattice systems,” Commun. Math. Phys. 31 (4), 291–294, 1973.
  • KMR Audenaert, “A sharp continuity estimate for the von Neumann entropy,” J. Phys. A Math. Theor. 40 (28) 8127-8137, 2007.
  • T.R. Gingrich, J.M. Horowitz, N. Perunov at al, “Dissipation Bounds All Steady-State Current Fluctuations,” Phys. Rev. Lett. 116 (12), 120601, 2016.
  • P. Pietzonka P, A. Barato, U. Seifert, “Universal bounds on current fluctuations,” Phys. Rev., E 93, 052145, 2016.
  • A. Moldavanov, “Theoretical Aspects of Radiative Energy Transport for Nanoscale System: Thermodynamic Uncertainty,” J. Comput. Theor. Trans, 50(3), 236-248, 2021.
  • N.W. Tschoegl, Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, 2000.
  • R. G. Lerner, G.L. Trigg, Encyclopaedia of Physics 3nd ed. Wiley-VCH Verlag, Weinheim, 1994.
  • L.S. Grant, W.R. Phillips, Electromagnetism, 2nd ed., Wiley. Manchester Physics Series, Hoboken, 2008.
  • R.A. Serway, J.W. Jewett, V. Peroomian, Physics for scientists and engineers with modern physics. 9th ed. Pacific Grove: Brooks Cole, 2014.
  • A. Moldavanov. “Energy Infrastructure of Evolution for System with Infinite Number of Links with Environment,” BioSystems, 213, 104607, 2022.
  • A.V. Moldavanov, “Analytical and Numerical Model for Evolution of Minimal Cell with Infinite Number of Energy Links,”: Proceedings Mathematical biology and bioinformatics, Pushino, Russia, 8, article # e16. doi: 10.17537 /icmbb20.15, 2020.
  • A. Moldavanov. “Randomized Continuity Equation Model of Energy Transport in Open System,” in AMSM 2017: Proceedings of the 2017 2nd International Conference on Applied Mathematics, Simulation and Modelling, 258 – 265, 2017.
  • D. J. C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, Cambridge, 2003.
  • J.W. Gibbs, Elementary Principles in Statistical Mechanics. New York: Dover Publications, 1960.
  • L. Benguigui, “The different paths to entropy,” arXiv.org Solid State Institute and Physics department Technion Israel Institute of Technology 32000 Haifa. Israel 1-32, 2012.
  • C. Marsh, “Introduction to Continuous Entropy,” Department of Computer Science, Princeton University.
  • B.P. Levin, Theoretical basics of statistical radio engineering. 3rd revised ed. Radio and communication, Мoscow, 1989.
  • R. Swenson, “Emergent attractors and the law of maximum entropy production: Foundations to a theory of general evolution,” Syst. Res. 6(3), 187–197, 1989.
  • J. Uffink, J. van Lith. “Thermodynamic uncertainty relations,” Found. Phys. 29 (5), 655-692, 1999.
  • J.S. Hsieh, Principles of Thermodynamics. Washington, D.C.: Scripta Book Company, 1975.
  • A.E. Shalyt-Margolin, A. Ya. Tregubovich. “Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics,” Mod. Phys. Lett. A. 19(1), 71-81, 2004.
  • G. Wilk, Z. Włodarczyk. “Application of nonextensive statistics to particle and nuclear physics,” Phys. A: Stat. Mech. Appl. 305 (1-2), 227-233. 2002.
  • J. Lindhard, Complementarity’ between energy and temperature, in The Lesson of Quantum Theory. edited by de Boer J, Dal E, Ulfbeck O., 99-112, North-Holland, Amsterdam, 1986.
  • A. Faigon, “Uncertainty and Information in Classical Mechanics Formulation. Common Ground for Thermodynamics and Quantum Mechanics,” https://arxiv.org/abs/quant-ph/0311153, 2007.
  • J.M. Horowitz, T.R. Gingrich, ”Thermodynamic uncertainty relations constrain non-equilibrium fluctuations,” Nat. Phys. 16, 15–20, 2020.
There are 43 citations in total.

Details

Primary Language English
Subjects Thermodynamics and Statistical Physics
Journal Section Research Articles
Authors

Andrei Moldavanov

Publication Date September 1, 2022
Published in Issue Year 2022 Volume: 25 Issue: 3

Cite

APA Moldavanov, A. (2022). Entropy of Open System with Infinite Number of Conserved Links. International Journal of Thermodynamics, 25(3), 47-53. https://doi.org/10.5541/ijot.1105040
AMA Moldavanov A. Entropy of Open System with Infinite Number of Conserved Links. International Journal of Thermodynamics. September 2022;25(3):47-53. doi:10.5541/ijot.1105040
Chicago Moldavanov, Andrei. “Entropy of Open System With Infinite Number of Conserved Links”. International Journal of Thermodynamics 25, no. 3 (September 2022): 47-53. https://doi.org/10.5541/ijot.1105040.
EndNote Moldavanov A (September 1, 2022) Entropy of Open System with Infinite Number of Conserved Links. International Journal of Thermodynamics 25 3 47–53.
IEEE A. Moldavanov, “Entropy of Open System with Infinite Number of Conserved Links”, International Journal of Thermodynamics, vol. 25, no. 3, pp. 47–53, 2022, doi: 10.5541/ijot.1105040.
ISNAD Moldavanov, Andrei. “Entropy of Open System With Infinite Number of Conserved Links”. International Journal of Thermodynamics 25/3 (September 2022), 47-53. https://doi.org/10.5541/ijot.1105040.
JAMA Moldavanov A. Entropy of Open System with Infinite Number of Conserved Links. International Journal of Thermodynamics. 2022;25:47–53.
MLA Moldavanov, Andrei. “Entropy of Open System With Infinite Number of Conserved Links”. International Journal of Thermodynamics, vol. 25, no. 3, 2022, pp. 47-53, doi:10.5541/ijot.1105040.
Vancouver Moldavanov A. Entropy of Open System with Infinite Number of Conserved Links. International Journal of Thermodynamics. 2022;25(3):47-53.