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Thermodynamic paths and stochastic order in open systems

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  • Lucia, Umberto

Abstract

The theorem of extremum entropy generation is related to the stochastic order of the paths inside the phase space; indeed, the system evolves, from an indistinguishable configuration to another one, on the most probable path in relation to the paths stochastic order. The result is that, at the stationary state, the entropy generation is maximal and, this maximum value is a consequence of the stochastic order of the paths in the phase space. Conversely, the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation for the open systems at the stationary states.

Suggested Citation

  • Lucia, Umberto, 2013. "Thermodynamic paths and stochastic order in open systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3912-3919.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:18:p:3912-3919
    DOI: 10.1016/j.physa.2013.04.053
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    References listed on IDEAS

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    1. Lucia, Umberto, 2013. "Stationary open systems: A brief review on contemporary theories on irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1051-1062.
    2. García-Morales, Vladimir & Pellicer, Julio, 2006. "Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 161-172.
    3. Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
    4. Sharma, Vivek & Kaila, Ville R.I. & Annila, Arto, 2009. "Protein folding as an evolutionary process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 851-862.
    5. Lucia, Umberto, 2007. "Irreversible entropy variation and the problem of the trend to equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 289-292.
    6. Lucia, Umberto, 2008. "Statistical approach of the irreversible entropy variation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3454-3460.
    7. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    8. Wang, Qiuping A., 2005. "Non-quantum uncertainty relations of stochastic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1045-1052.
    9. Lucia, Umberto, 2012. "Irreversibility in biophysical and biochemical engineering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5997-6007.
    10. Lucia, Umberto, 2009. "Irreversibility, entropy and incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4025-4033.
    11. Lucia, Umberto, 2013. "Entropy and exergy in irreversible renewable energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 20(C), pages 559-564.
    12. Lucia, U., 2012. "Maximum or minimum entropy generation for open systems?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3392-3398.
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    Citations

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    Cited by:

    1. Lucia, Umberto, 2014. "Entropy generation and cell growth with comments for a thermodynamic anticancer approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 107-118.
    2. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    3. Lucia, Umberto, 2014. "Entropy generation: Minimum inside and maximum outside," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 61-65.
    4. Mook, W.T. & Aroua, M.K. & Issabayeva, G., 2014. "Prospective applications of renewable energy based electrochemical systems in wastewater treatment: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 38(C), pages 36-46.
    5. Lucia, Umberto, 2016. "Considerations on non equilibrium thermodynamics of interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 314-319.
    6. Lucia, Umberto, 2016. "Second law considerations on the third law: From Boltzmann and Loschmidt paradox to non equilibrium temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 121-128.
    7. Bor-Sen Chen & Xiangyun Lin & Weihai Zhang & Tianshou Zhou, 2018. "On the System Entropy and Energy Dissipativity of Stochastic Systems and Their Application in Biological Systems," Complexity, Hindawi, vol. 2018, pages 1-18, December.
    8. Lucia, Umberto & Ponzetto, Antonio & Deisboeck, Thomas S., 2015. "A thermodynamic approach to the ‘mitosis/apoptosis’ ratio in cancer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 246-255.
    9. Umberto Lucia & Giulia Grisolia, 2022. "Thermodynamic Definition of Time: Considerations on the EPR Paradox," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    10. Umberto Lucia & Giulia Grisolia, 2018. "Cyanobacteria and Microalgae : Thermoeconomic Considerations in Biofuel Production," Energies, MDPI, vol. 11(1), pages 1-16, January.
    11. Lucia, Umberto, 2016. "Econophysics and bio-chemical engineering thermodynamics: The exergetic analysis of a municipality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 421-430.
    12. Lucia, Umberto, 2014. "Entropy generation and the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 256-260.
    13. Lucia, Umberto, 2014. "Overview on fuel cells," Renewable and Sustainable Energy Reviews, Elsevier, vol. 30(C), pages 164-169.
    14. Umberto Lucia, 2014. "The Gouy-Stodola Theorem in Bioenergetic Analysis of Living Systems (Irreversibility in Bioenergetics of Living Systems)," Energies, MDPI, vol. 7(9), pages 1-23, September.
    15. Lucia, Umberto, 2014. "Entropy generation approach to cell systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 1-11.
    16. Lucia, Umberto & Grisolia, Giulia, 2017. "Unavailability percentage as energy planning and economic choice parameter," Renewable and Sustainable Energy Reviews, Elsevier, vol. 75(C), pages 197-204.
    17. Lucia, Umberto, 2015. "Quanta and entropy generation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 115-121.

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