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Abiogenesis and the Second Law of Thermodynamics

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Advances in Quantum Systems in Chemistry, Physics, and Biology (QSCP 2018)

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 32))

Abstract

Abiogenesis, life arising from non-living matter, is reconsidered. A historic account is given from Darwin to the present with special consideration of the incipient relationship between quantum theory and life processes. Recent ideas relating to the spontaneous emergence of life are considered and evaluated, including the work on self-organizing systems by Ilya Prigogine and the Brussels-Austin School. The second law is commensurate with chemical evolution, but is incapable of explaining the mechanism behind the selection of specific polymers from an infinitude of molecular specimens. We attest abiogenetic life processes originating from a quantum chemical material world. A Gibbs free energy formulation is derived ab initio conceding non-equilibrium evolutions and open system self-organization. Correlated Dissipative Structures, CDS, combine quantum-thermal correlations at precise temperatures commensurate with their adaptive time scales, constituting CDE, a Correlated Dissipative Ensemble. The theory suggests an objective communication principle reminding of a Call-Centre-Poisson point process. The self-referential structure applies directly to biological systems, suggesting a fundamental quantum-chemistry life-principle incorporating evolution of the whole biosphere without contradicting the objectivity of physical laws.

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Notes

  1. 1.

    See e.g. an interesting discussion of Darwin’s stance on spontaneous generation in [1].

  2. 2.

    The story is quoted in Brown’s Bernal biography, see Ref. [5].

  3. 3.

    According to the reviewer [13], the book comes as a real surprise to those comfortable with the view that the scientific problems of abiogenesis are mostly resolved.

  4. 4.

    These thermally excited modes are identified as Jordan blocks, converting states to sequences of transitions.

  5. 5.

    Mayr introduced teleonomic processes, on par, but thus far not accounted for, by known physical laws, as follows: A teleonomic process or behaviour is one that owes its goal-directedness to the influence of an evolved program.

  6. 6.

    Monod struggled with an epistemological contradiction, i.e. objectivity set against the need for teleonomy in biology stating: In fact the central problem of biology lies within this contradiction.

  7. 7.

    The discussion took place at the Canary Islands in 2004, while the transcripts did not appear in print until 2008, see [25] and in particular the contributions by Paul Davies and Howard Wiseman.

  8. 8.

    In the foreword to [25] Sir Roger Penrose asks the question: Is it merely the complexity of biology that gives living systems their special qualities and if so, how does this complexity come about? Or are the special features of strongly quantum-mechanical system in some way essential? Penrose’s answer is well-known, but we will not discuss his “Orch OR” theory, nor in detail Tegmark’s decoherence argument.

  9. 9.

    By many considered the father of quantum chemistry, see [26] for rationales.

  10. 10.

    The debate whether the Nobel Prize awarded work on density functional theory, DFT, should be considered ab initio will not be discussed here. Yet, DFT is definitely epistemic in nature.

  11. 11.

    Bishop has analysed the work of the Brussels-Austin Group [29] with particular focus on the definitions and mathematical extensions to rigged Hilbert spaces and its applications to concrete mathematical systems.

  12. 12.

    Bricmont refers to Lanford’s original derivation of Boltzmann’s equation [33].

  13. 13.

    Lanford’s theorem in the case of N hard spheres was extended in [34]. The review [35] nevertheless concludes: Boltzmann’s 1872 effort, to conciliate microscopic time-reversible dynamics with increase of entropy and trend to equilibrium, still remains as a source of challenging mathematical problems.

  14. 14.

    It is hard to evaluate general statements made here, since the fundamental difference between CM and QM at the end of the day turns out to be significant.

  15. 15.

    The non-Hermitian extension permits higher order singularities affecting the time evolution of the CES.

  16. 16.

    See e.g. Wiseman in [25].

  17. 17.

    Cf. the Koopman representation employed in the Prigogine sub-dynamics. For more details see [29].

  18. 18.

    The original Technical Note, dated May 1, 1962, from the Uppsala Quantum Chemistry Group is available on internet and authenticated as ASTIA DOCUMENT No: AD No. 296970. The story behind the lost manuscript and the progress of ODLRO has been told at numerous occasions, see [26] for more details.

  19. 19.

    Other physical areas represented in the book were also laser physics, quantum optics, quantum information and subatomic physics.

  20. 20.

    Ref. [45] was originally published in 2005 in different form in German by C. Bertelsmann. Germany, as Einstein Spuk: Teleportation und weitere Mysterien der Quantenphysik.

  21. 21.

    Cf. the statements by Paul Davies in [25].

  22. 22.

    Note that the notion of microscopic reversibility means different things in CM and QM.

  23. 23.

    Cf. Bricmont’s comments in the previous section and associated footnotes.

  24. 24.

    Although the complete state space dimension might be infinite, the relevant degrees of freedom using partitioning technique turns out to be finite. Employing the thermodynamic limit is another source of irreversibility.

  25. 25.

    The limit is usually interpreted as the course-grained limit with the time being smaller than a process-defined relaxation time, \(\tau_{\text{rel}}\), but still large enough to randomize the phases. The Prigogine sub-dynamics does not contain this assumption.

  26. 26.

    We have naively assumed a finite number of reference states, which in a more refined treatment must be coupled to a continuum, which technically can be formulated by Löwdin’s partitioning technique [49] or the Nakajima–Zwanzig equation [50, 51].

  27. 27.

    Wiener, the father of Cybernetics, introduced feed-back and learning as mechanisms for information and communication in evolving organizations. See more on Communication Simpliciter in later sections.

  28. 28.

    Stated by the Swedish Chemistry Nobel Laureate The Svedberg, see also the AIM magazine in Phase below.

  29. 29.

    The graduate program, producing 35 Ph.D’s, was sponsored by the Swedish Foundation for Strategic research. The AIM Magazine, InPhase: Bridging the Gap between Academia and Industry is available from the author on request.

  30. 30.

    The nature of these degrees, paired fermionic or bosonic etc., will be discussed later.

  31. 31.

    This might appear as an unnecessary limitation. However, assigning instead \(g\) degrees of freedom, the result becomes simply that \(n\) will be replaced by \(n/g\) in Eq. (4.6). Without restricting the formulation one might refer to \(n^{\prime} = n/g\) as the relevant degrees of freedom defining \(UD\left( {n^{\prime}} \right)\), provided \(n^{\prime}/4\pi \gg 1\).

  32. 32.

    Note that \(\sigma_{\text{tot}}\) cancels out in the final relation and that the factor \(4\pi\) occurs since the outgoing flux of \(UD\left( n \right)\) is defined per solid angle. In biological systems the number \(n\) gets important since it conveys crucial information regarding the performance of each CES. In such cases the quality index \(n\) will be explicitly denoted separating it from other technological or artificial intelligence devices.

  33. 33.

    This is usually referred to as analytic continuation onto the second unphysical Riemann sheet.

  34. 34.

    For instance the relation between kinetic and potential energies, see relevant discussions in Ref. [26].

  35. 35.

    Cf. the concept of star-unitary transformations introduced by the Brussels-Austin School.

  36. 36.

    This imparts the occurrence of the irreducible Jordan normal form of the operator representation, where the order of the largest block defines the Segrè characteristics corresponding to the actual degeneracy.

  37. 37.

    Any matrix can be brought to complex symmetric form.

  38. 38.

    Note that a resonance may come arbitrarily close to the real axis and still be classified as being located on the second sheet.

  39. 39.

    The partition of the propagator into its retarded-advanced parts will be crucial as it imposes a separation of positive-negative times corresponding to the lower-upper parts respectively of the complex energy plane.

  40. 40.

    The Swedish mathematician Torsten Carleman extended the Fourier transformation by splitting the integral into two parts with the variable \(z\) being complex. This generalization is well described in Lützens’s Studies in the History of Mathematics and Physical Sciences No. 7 [67].

  41. 41.

    For a simple introduction see Ref. [68] and footnote 36.

  42. 42.

    This is a technical problem, yet of crucial importance. Suffice it to say that Nelson’s class of analytic vectors, dense in Hilbert space, is a key ingredient in the proof of the Balslev-Combes theorem [37], see also Ref. [70] for more details on its use.

  43. 43.

    The proof involves the notion of quasi-isometry. The problem is due to the fact that the numerical range of a complex scaled attractive Coulomb potential cannot be proven to be restricted to the lower complex halfplane, a necessary and a sufficient condition for the fulfillment of the Hille-Yosida theorem [20].

  44. 44.

    The discussions occur in an interdisciplinary poll [74] that concerns the reconciliation of profoundly conflicting facts regarding time and the fundamental processes going on in the world.

  45. 45.

    The evolution of \(UD\left( n \right)\) turns out to be Poissonian the loss of memory is here implicit.

  46. 46.

    See the definitions introduced by Husimi [41].

  47. 47.

    In the reduced representation one could employ the reduced Hamiltonian [44], and in a thermalized picture one might also include the chemical potential.

  48. 48.

    We will denote the spatial coordinates with a vector notation, i.e. \(\vec{x}_{k}\).

  49. 49.

    The electronic- and the nuclear systems are entangled, which, as we will see, provides a way to go beyond the Born-Oppenheimer approximation [17, 21, 70].

  50. 50.

    The normalization factor is not explicitly shown in the antisymmetric wedge product symbolized by \(\wedge\).

  51. 51.

    In fact \(\lambda_{T} = \lambda_{S}\), displaying that all eigenvalues are degenerate except \(\lambda_{L}\).

  52. 52.

    The transformation \(\varvec{B}\) becomes a key quantity, see also footnote 55 and the next section.

  53. 53.

    The story is detailed in Ref. [78].

  54. 54.

    As can also be deduced from statistical arguments [77], one finds \(\lambda_{S} = \frac{{N\left( {N - 2} \right)}}{{4n\left( {n - 1} \right)}}; \lambda_{L} = \frac{N}{2} - \frac{{N\left( {N - 2} \right)}}{4n}\).

  55. 55.

    It is interesting to note that \(\varvec{B}\) and \(\varvec{B}^{\dag }\) occur both in connection with (6.9) and (6.15). This coincidence is not obvious.

  56. 56.

    Cf. a random phase system.

  57. 57.

    The mirror theorem was revived by Carlson and Keller [85] and generalized by Löwdin [68, 78]. The mapping between the two-particle electronic coordinate, characterized by the internal and the center-of-mass of the pair, and the apposite nuclear degree of freedom is studied in [86].

  58. 58.

    The present mapping appears incompatible since in general \(N < 2n\). This is automatically taken care of by the mirror theorem, since the extra eigenvalues in the larger space dimension are filled out by zeros.

  59. 59.

    Note that we have left the original coherent wavefunction in (6.5) for the statistical derivation [77] that provides the necessary link with an original ensemble representative density matrix technically derivable through an appropriate sub-dynamics.

  60. 60.

    The stringent philosopher, Rosenberg [87], views biological issues within the same epistemological framework as the philosophy of physics, primarily based on the second law. It is of course beyond this summary to render a fair and ample account of the detailed ingredients that goes into such a stance.

  61. 61.

    For the Poisson distribution the variance equals the mean.

  62. 62.

    Equations (4.6) and (4.10) do not guarantee that the UD condition holds. In this particular case the Brownian-like motion contains no information.

  63. 63.

    Note that different situations lead to various Jordan forms and their Segré characteristics as well as differing magnitudes of \(\lambda_{L} , \lambda_{S}\). For simplicity we have made the choice (6.22).

  64. 64.

    Communication taken in a restricted sense, i.e. without semantics employing only syntax and pragmatics.

  65. 65.

    Attaching the name ”Gödel” to the network has been explained in several articles [89, 95], see e.g. Chap. 4 in [95].

  66. 66.

    The matrix (8.12) has a direct link with Gödel’s self-referential paradox, see footnote 65.

  67. 67.

    As it is usually projected today, for more details, see [70, 95, 99]. Note that (8.16) also may be written as a secular equation of a complex symmetric matrix, see [99, 100].

  68. 68.

    In retrospect the singularity shares the same self-referential conundrum as we associate with Gödel’s incompleteness theorem [89, 95].

  69. 69.

    The formula (28) in [99] has been corrected in [100].

  70. 70.

    There is no relative motion here, then again Sects. 6 and 7 applies. A discussion, including the Kerr metric and a possible quantum analogue of Penrose’s cosmic censorship hypothesis, can be found in [70].

  71. 71.

    The mirror relation between N, the number of fermions, and n, the number of nuclear centers naturally disappears in the QBH, but a bosonic analysis nevertheless yields a number, see [77].

  72. 72.

    Penrose discusses space-like futures with massless particles calling our Universe an aeon in an endless sequence of aeons.

  73. 73.

    In this formulation concepts such as Hawking radiation and the Bekenstein-Hawking entropy have not been considered here. Whether and how they might become applicable also in a quantum theoretical description remain a topic for the future.

  74. 74.

    Note that communication is here taken in a restricted sense in concert with the concept of semiology which excludes semantics, one of three components of semiotics, see also [24, 92].

  75. 75.

    Regarding self-references and Gödel see footnotes 65, 66, 68 and in particular chapter 4 in [95].

  76. 76.

    Note that Chalmers’ concept of the Hard Problem presupposes a dualistic attitude. Various recent suggestions display ‘the long and winding road’ from monism to dualism.

References

  1. Peretó J, Bada LB, Lazcano A (2009) Charles Darwin and the origin of life. Orig Life Evol Biosph 39(5):395

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  2. Miller SL (1953) A production of amino acids under possible primitive earth conditions. Science 117(3046):528

    Article  CAS  Google Scholar 

  3. Miller SL, Urey HS (1959) Organic compound synthesis on the primitive earth. Science 130(3370):245

    Article  CAS  Google Scholar 

  4. Trainer MG (2013) Atmospheric prebiotic chemistry and organic hazes. Curr Org Chem 17:1710

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Brown A (2005) J. D. Bernal: the sage of science. Oxford University Press, Oxford

    Google Scholar 

  6. Bernal JD (1967) The physical basis of life. Wiedenfeld and Nicholson, London

    Google Scholar 

  7. Oparin AI (1924) Proiskhozhdenie zhizny. Izd. Moskowhii Rabochii, Moscow

    Google Scholar 

  8. Oparin AI (1938) The origin of life. Macmillan, New York

    Google Scholar 

  9. Haldane JBS (1929) The origin of life. The Rationalist Annual, Watts CA, pp 3–10

    Google Scholar 

  10. Cairns-Smith AG (1982) Genetic takeover: and the mineral origins of life. Cambridge University Press, Cambridge

    Google Scholar 

  11. Hoyle F, Wickramasinge NC (1981) Evolution from space. J M Dent, London

    Google Scholar 

  12. Thaxton CB, Bradley WL, Olson RL (1984) The mystery of life’s origin: reassessing current theories. Philosophical Library Inc, New York

    Google Scholar 

  13. Jekel JF (1985) The mystery of life’s origin: reassessing current theories. Review. Yale J Biol Med 58(4):407

    PubMed Central  Google Scholar 

  14. Prigogine I (1996) The end of certainty: time, chaos, and the new laws of nature. The Free Press, New York

    Google Scholar 

  15. Obcemea CH, Brändas EJ (1983) Analysis of Prigogine’s theory of subdynamics. Ann Phys 151:383

    Article  CAS  Google Scholar 

  16. Atmanspacher H, Bishop RC, Amann A (2001) Extrinsic irreversibility in probabilistic dynamical laws. In: Khrennikov A (ed) Proceedings of the conference foundations of probability and physics, QP-PQ: Quantum probability and white noise analysis, vol XIII, p 50

    Google Scholar 

  17. Brändas EJ (2017) The origin and evolution of complex enough systems. In: Tadjer A, Pavlov R, Maruani J, Brändas EJ, Delgado-Barrio G (eds) Quantum systems in physics, chemistry, and biology, vol 30. Springer, Berlin, p 413

    Google Scholar 

  18. Nicolis G, Prigogine I (1977) Self-Organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York

    Google Scholar 

  19. Eigen M (1971) Self-organization of matter and the evolution of biological macromolecules. Die Naturwissenshaften 64:465

    Article  Google Scholar 

  20. Kumicak J, Brändas EJ (1993) Complex scaling and Lyapunov converters. Int J Quant Chem 46:391

    Article  Google Scholar 

  21. Brändas EJ (2012) Examining the limits of physical theory: analytical principles and logical implications. Adv Quant Chem 63:33

    Article  CAS  Google Scholar 

  22. Mayr E (2004) What makes biology unique?. Cambridge University Press, New York

    Book  Google Scholar 

  23. Monod J (1971) Chance and necessity: an essay on the natural philosophy on modern biology. Alfred A. Knopf Inc., New York

    Google Scholar 

  24. Brändas EJ (2018) Molecular theory of the genetic code. Mol Phys 116(19–20):2622

    Article  CAS  Google Scholar 

  25. Abbott D, Davies PCW, Pati KP (2008) Quantum aspects of life. Imperial College Press, London

    Book  Google Scholar 

  26. Brändas EJ (2017) Löwdin—father of quantum chemistry. Mol Phys 115(17–18):1

    Google Scholar 

  27. Prigogine I (1980) From being to becoming time, and complexity in physical sciences. W. H. Freeman and Company, San Francisco

    Google Scholar 

  28. Atmanspacher H, Primas H (2003) Epistemic and ontic quantum realities. In: Castell L, Ischebeck O (eds) Time, quantum and information. Springer, Berlin, Heidelberg, p 301

    Chapter  Google Scholar 

  29. Bishop RC (2004) Non-equilibrium statistical mechanics, Brussels-Austin style. Stud History Philos Mod Phys 35:1

    Article  Google Scholar 

  30. Brändas EJ (1993) Resonances and microscopic irreversibility: an introduction. Int J Quant Chem 46:339

    Article  Google Scholar 

  31. Earley JE Sr (2006) Some philosophical influences on ilya Prigogine’s statistical mechanics. Found Chem 8(3):271

    Article  Google Scholar 

  32. Bricmont J (1995) Science of chaos or chaos in science. Physicalia Magazine 17:159

    Google Scholar 

  33. Lanford OE (1975) Time evolution of large classical systems. Dynamical systems, theory and applications. Lecture notes in physics, vol 38, p 1

    Google Scholar 

  34. Gallagher I, Saint-Raymond L, Texier B (2013) From Newton to Boltzmann: hard spheres and short-range potentials. In: Zürich lectures in advanced mathematics. European Mathematical Society, Zürich

    Google Scholar 

  35. Simonella S, Spohn H (2015) Bull Am Math Soc 52(3):533

    Article  Google Scholar 

  36. Brändas EJ, Chatzidimitriou-Dreismann CA (1995) Fundamentals, logical structure and unification of natural sciences. Int J Quant Chem 53:95

    Article  Google Scholar 

  37. Balslev E, Combes JM (1971) Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Commun Math Phys 22:280

    Article  Google Scholar 

  38. Nicolaides CA, Brändas EJ (eds) (2010) Unstable states in the continuous spectra, part I: analysis, concepts, methods, and results. Adv Quant Chem 60; ibid. (2012) Unstable states in the continuous spectra, part II: interpretation, theory and applications. 63

    Google Scholar 

  39. Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press, New York

    Book  Google Scholar 

  40. Löwdin P-O (1964) Some aspects of quantum biology. In: Biopolymers symposia, vol 1, p 293

    Google Scholar 

  41. Husimi K (1940) Some formal properties of the density matrix. Proc Phys Math Soc Jpn 22:246

    Google Scholar 

  42. Sasaki F (1965) Eigenvalues of fermion density matrices. Phys Rev 138B:1338

    Article  Google Scholar 

  43. Yang CN (1962) Concept of off-diagonal long-range order and the quantum phases of liquid helium and of superconductors. Rev Mod Phys 34:694

    Article  CAS  Google Scholar 

  44. Coleman AJ (1963) Structure of fermion density matrices. Rev Mod Phys 35:668

    Article  Google Scholar 

  45. Zeilinger A (2010) Dance of the photons from einstein to quantum teleportation. Farrar Strauss and Giroux, New York

    Google Scholar 

  46. Crooks GE (1999) Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys Rev E 60:2721

    Article  CAS  Google Scholar 

  47. Jarzynski C (2007) Equilibrium free-energy differences from nonequilibrium measurements: a master equation approach. Phys Rev E 56:5018

    Article  Google Scholar 

  48. England JL (2013) Statistical physics of self-replication. J Chem Phys 138:121923

    Article  CAS  Google Scholar 

  49. Löwdin P-O (1951) A note on the quantum-mechanical perturbation theory. J Chem Phys 19:1396

    Article  Google Scholar 

  50. Nakajima S (1958) On quantum theory of transport phenomena—steady diffusion. Prog Theor Phys 20:948

    Article  Google Scholar 

  51. Zwanzig R (1960) Ensemble method in the theory of irreversibility. J Chem Phys 33:1338

    Article  CAS  Google Scholar 

  52. Huang K (1963) Statistical mechanics. Wiley, New York

    Google Scholar 

  53. Barrett HH, Myers KJ (2004) Foundations of image science. Wiley, Hoboken New Jersey

    Book  Google Scholar 

  54. Belkić D (2005) Quantum-mechanical signal processing and spectral analysis. Institute of Physics Series in Atomic- and Molecular Physics, Institute of Physics Publishing, Bristol

    Google Scholar 

  55. Levitina T, Brändas EJ (2009) Filter diagonalization: filtering and postprocessing with prolates. Comp Phys Comm 180:1448

    Article  CAS  Google Scholar 

  56. Wiener N (1948) Cybernetics or control and communication in the animal and the machine. Wiley, New York

    Google Scholar 

  57. Brändas EJ (1997) Resonances and dilatation analyticity in Liouville space. Adv Chem Phys 99:211

    Google Scholar 

  58. Brändas EJ (2003) New perspectives in theoretical chemical physics. Adv Quant Chem 42:383

    Article  Google Scholar 

  59. Gibbons M, Limoges C, Nowotny H, Schwartzman S, Scott P, Trow M (1994) The new production of knowledge. The dynamics of science and research in contemporary societies. Sage Publications Ltd., London

    Google Scholar 

  60. Feder T (2000) Physics graduate programs train students for industrial careers. Phys Today 53(8):39

    Article  Google Scholar 

  61. Boström R, Brändas E, Kullander S (1998) Promoting university—industry links by a new type of Ph.D. education: The AIM Graduate School. In: Conference proceedings, Vienna, 4–6 November 1998 ESA, vol 432. Academic and Industrial Cooperation in Space Research, p 181

    Google Scholar 

  62. Brändas EJ (2003) Advanced instrumentation and measurements: a research education programme at Uppsala University. Eur Phys Educ Netw 7:147

    Google Scholar 

  63. Rittby M, Elander E, Brändas E, Barany A (1984) Resonance structure in charge transfer cross sections: an application to the N3+ + H → N2+ + H+ reaction. J Phys B: At Mol Phys 17:L677

    Article  CAS  Google Scholar 

  64. Brändas EJ (1984) Time evolution of chemical systems far from equilibrium. In: Lecture Notes in Physics, vol 211, p 307

    Google Scholar 

  65. Enss V (1984) Summary of the conference and some open problems. In: Lecture Notes in Physics, vol 211, p 351

    Google Scholar 

  66. Carleman T (1944) L’Intégrale de Fourier et questions que s’y rattachent. Mittag-Leffler Institute of Publications, Uppsala

    Google Scholar 

  67. Lützen J (1982) The prehistory of the theory of distributions. Springer, New York

    Google Scholar 

  68. Löwdin P-O (1998) Linear algebra for quantum theory. Wiley, New York

    Google Scholar 

  69. Nelson E (1959) Analytic vectors. Ann Math 70:572

    Article  Google Scholar 

  70. Brändas EJ (2012) Time asymmetry and the evolution of physical laws. In Hoggan PE, Brändas EJ, Maruani J, Piechuch P, Delgado-Barrio G (eds) Advances in the theory of quantum systems in chemistry and physics, vol 22, Springer, Berlin, p 3

    Google Scholar 

  71. Brändas EJ, Antoniou IE (1993) On the positivity condition in the non-unitary transformation theory of irreversibility. Int J Quant Chem 46:419

    Article  Google Scholar 

  72. Kumicàk J, Brändas E (1993) Some aspects of approach to equilibrium in classical and quantum systems. Int J Quant Chem 32:669

    Article  Google Scholar 

  73. Brändas EJ, Chatzidimitriou-Dreismann CA (1989) Creation of long range order in amorphous condensed systems. Lecture Notes in physics, vol 325. Springer, Berlin, p 485

    Google Scholar 

  74. Halliwell JJ (1994) Quantum cosmology and time asymmetry. In: Halliwell JJ, Pérez-Mercader J, Zurek WH (eds) Physical origins of time asymmetry. Cambridge University Press, Cambridge, p 369

    Google Scholar 

  75. Brändas EJ (2013) Arrows of time and fundamental symmetries in chemical physics. Int J Quant Chem 113:173

    Article  CAS  Google Scholar 

  76. Hehenberger H, McIntosh HV, Brändas E (1974) Weyl’s theory applied to the Stark effect in the hydrogen atom. Phys Rev A 10(5):1494

    Article  CAS  Google Scholar 

  77. Brändas EJ, Chatzidimitriou-Dreismann CA (1990) On the connection between certain properties of the second-order reduced density matrix and the occurrence of coherent-dissipative structures in disordered condensed matter. Int J Quant Chem 40:649

    Article  Google Scholar 

  78. Löwdin P-O (1987) Some aspects of the development of the theory of reduced density matrices and the representability problem. In: Erdahl R, Smith VH Jr (eds) Density matrices and density functionals. Reidel, Dordrecht, p 21

    Chapter  Google Scholar 

  79. Dunne LJ, Brändas EJ, Cox H (2017) High-temperature superconductivity in strongly correlated electronic systems. Adv Quant Chem 74:183

    Article  CAS  Google Scholar 

  80. Leggett AJ (2006) Quantum liquids, bose condensation and cooper pairing in condensed matter systems. Oxford University Press, Oxford

    Google Scholar 

  81. Coleman AJ (1987) Reduced density matrices: 1929–1989. In: Erdahl R, Smith VH Jr (eds) Density matrices and density functionals. Reidel, Dordrecht, p 5

    Chapter  Google Scholar 

  82. Brändas E, Froelich P (1977) Continuum orbitals, complex scaling and the extended virial theorem. Phys Rev A 16:2207

    Article  Google Scholar 

  83. Reid CE, Brändas EJ (1989) On a theorem for complex symmetric matrices and its relevance in the study of decay phenomena. In: Lecture notes in chemistry, vol 325. Springer, Berlin, p 475

    Google Scholar 

  84. Brändas EJ (2009) A theorem for complex symmetric matrices revisited. Int J Quant Chem 109:28960

    Google Scholar 

  85. Carlson BC, Keller JM (1961) Eigenvalues of density matrices. Phys Rev 121:659

    Article  Google Scholar 

  86. Brändas EJ, Hessmo B (1998) Indirect Measurements and the mirror theorem. In: Lecture notes in physics, vol 504, p 359

    Google Scholar 

  87. Rosenberg A (1985) The structure of biological sciences. Cambridge University Press, Cambridge

    Google Scholar 

  88. Rosenberg A (2011) The atheists guide to reality: enjoying life without illusions. W W Norton & Co., New York

    Google Scholar 

  89. Brändas EJ (2011) Gödelian structures and self-organization in biological systems. Int J Quant Chem 111:1321

    Article  CAS  Google Scholar 

  90. Crick F, Koch C (1990) Towards a neurobiological theory of consciousness. Semin Neurosci 2:263

    Google Scholar 

  91. Koch C, Massimini M, Boly M, Tononi G (2016) Neural correlates of consciousness: progress and problems. Nat Rev Neurosci 17:307

    Article  CAS  PubMed  Google Scholar 

  92. Brändas EJ (2019) Molecular foundation of evolution. Adv Quant Chem 78:193

    Google Scholar 

  93. Trehub A (1991) The cognitive brain. MIT Press, London

    Google Scholar 

  94. Trehub A (2007) Space, self, and the theatre of consciousness. Conscious Cogn 16:310

    Article  PubMed  Google Scholar 

  95. Brändas EJ (2015) A zero energy universe scenario: from unstable chemical states to biological evolution and cosmological order. In: Nascimento MAC, Maruani J, Brändas EJ, Delgado-Barrio G (eds) Frontiers in quantum methods and applications in chemistry and physics, vol 29. Springer, Dordrecht, p 247

    Chapter  Google Scholar 

  96. Maruani J (2016) The Dirac equation: from quantum chemistry to holistic cosmology. J Chin Chem Soc 63:33

    Article  CAS  Google Scholar 

  97. Mersini-Houghton L (2014) Backreaction of Hawking radiation on a gravitationally collapsing star I: black holes? Phys Lett B 738:61

    Article  CAS  Google Scholar 

  98. Mersini-Houghton L (2015) Back reaction of the Hawking radiation flux in Unruh’s vacuum on a gravitationally collapsing star II. arXiv:1409.1837v2 [hep-th]

  99. Brändas EJ (2016) A comment on background independence in quantum theory. J Chin Chem Soc 63:11

    Article  CAS  Google Scholar 

  100. Brändas EJ (2018) A simple communication hypothesis: the process of evolution reconsidered. In: Wang YA, Thachuk M, Krems R, Maruani J (eds) Concepts, methods and applications of quantum systems in chemistry and physics, vol 31. Springer, Cham, p 381

    Chapter  Google Scholar 

  101. Penrose R (2010) Cycles of time an extraordinary new view of the new universe. The Bodley Head, London

    Google Scholar 

  102. Schrödinger E (1992) What is life? with mind and matter & autobiographical sketches. Cambridge University Press, Cambridge

    Book  Google Scholar 

  103. Tsekov R, Lensen MC (2013) Brownian motion and temperament of living cells. Chin Phys Lett 30:070501

    Article  Google Scholar 

  104. Chalmers DJ (1996) The conscious mind in search of a fundamental theory. Oxford University Press, Oxford

    Google Scholar 

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Acknowledgements

I am grateful to the Chair of QSCP XXIII, Prof. Liliana Mammino, and the Co-Chair Jean Maruani for generously allowing me to present this work in the present proceedings from the meeting. My indebtedness for constructive suggestions and recommendations goes to Prof. Alia Tadjer and Prof. Jean Maruani. This work has over time been supported by the Swedish Natural Science Research Council, the Swedish Foundation for Strategic Research, The European Commission and the Nobel Foundation.

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  1. Department of Chemistry, Uppsala University, Uppsala, Sweden

    Erkki J. Brändas

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  1. Erkki J. Brändas
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Correspondence to Erkki J. Brändas .

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Editors and Affiliations

  1. School of Mathematical and Natural Sciences, University of Venda, Thohoyandou, South Africa

    Liliana Mammino

  2. Istituto di Scienze e Tecnologie Moleculari, Consiglio Nazionale delle Ricerche, Milan, Italy

    Davide Ceresoli

  3. Laboratoire de Chimie Physique, CNRS & UPMC, Paris, France

    Jean Maruani

  4. Department of Chemistry, Uppsala University, Uppsala, Sweden

    Erkki Brändas

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Brändas, E.J. (2020). Abiogenesis and the Second Law of Thermodynamics. In: Mammino, L., Ceresoli, D., Maruani, J., Brändas, E. (eds) Advances in Quantum Systems in Chemistry, Physics, and Biology. QSCP 2018. Progress in Theoretical Chemistry and Physics, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-34941-7_15

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