Papers

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Sharma V, Annila A. Natural process - Natural selection. Biophys. Chem. 2007 127, 123-128. (pdf) https://doi:10.1016/j.bpc.2007.01.005
Evolution is given by the principle of increasing entropy as an equation of motion derived from statistical physics of open systems.

Grönholm T, Annila A. Natural distribution. Math. Biosci. 2007 210, 659-667. (pdf) https://doi:10.1016/j.mbs.2007.07.004
Ubiquitous power laws and lognormal distributions are found to follow from the 2nd law of thermodynamics.

Kaila VRI, Annila A. Natural selection for least action. Proc. R. Soc. A. 2008 464, 3055-3070. (pdf) https://doi:10.1098/rspa.2008.0178
The principle of least action is shown to be equivalent to the 2nd law of thermodynamics and Newton's 2nd law.

Jaakkola S, Sharma V, Annila A. Cause of chirality consensus. Curr. Chem. Biol. 2008 2, 53-58. (pdf) https://doi:10.2174/2212796810802020153
Standards of natural and artificial are found to follow from the 2nd law of thermodynamics.

Jaakkola S, El-Showk S, Annila A. The driving force behind genomic diversity. Biophys. Chem. 2008 134, 232-238, (136) (pdf) arXiv:0807.0892
Genomic diversity as any other form of variety is found to follow from the 2nd law of thermodynamics.

Würtz P, Annila A. Roots of diversity relations. J. Biophys. 2008 ID 654672, 8 p. (pdf) https://doi:10.1155/2008/654672. arXiv:0906.0251
Species-area and other systemic relationships are found to follow from the 2nd law of thermodynamics.

Annila A, Annila E. Why did life emerge? Int. J. Astrobio. 2008 7, 293-300. (pdf) https://doi:10.1017/S1473550408004308
Life in its entirety is a natural process resulting from the least-time free energy consumption.

Tuisku P, Pernu TK, Annila A. In the light of time. Proc. R. Soc. A. 2009 465, 1173-1198. (pdf) https://doi:10.1098/rspa.2008.0494
A flow of time relates to a quantized flow of energy from a system to its surroundings and vice versa.

Karnani M, Annila A. Gaia again. BioSystems 2009 95, 82-87. (pdf) https://doi:10.1016/j.biosystems.2008.07.003а
Global homeostasis is a maximum entropy state equivalent to a free energy minimum state.

Sharma V, Kaila VRI, Annila A. Protein folding as an evolutionary process. Physica A 2009 388, 851-862. (pdf) https://doi.org/10.1016/j.physa.2008.12.004
Protein folding is shown to be an inherently intractable process as any other evolutionary course.

Annila A, Kuismanen E. Natural hierarchy emerges from energy dispersal. BioSystems 2009 95, 227-233. (pdf) https://doi:10.1098/rspa.2009.0063
Rise of hierarchy is a consequence of the least-time free energy consumption.

Karnani M, Pääkkönen K, Annila A. The physical character of information. Proc. R. Soc. A. 2009 465, 2155-2175. (pdf) https://doi.org/10.1098/rspa.2009.0063
Information is physical due to its representations that are subject to the 2nd law of thermodynamics.

Annila A, Salthe S. Economies evolve by energy dispersal. Entropy 2009 11, 606-633. (pdf) https://doi:10.3390/e110406067
Economies are energy transduction systems that follow the 2nd law of thermodynamics.

Würtz P, Annila A. Ecological succession as an energy dispersal process. BioSystems 2010 100, 70-78. (pdf) https://doi.org/10.1016/j.biosystems.2010.01.004
Succession of a system from one state to another is a manifestation of the 2nd law of thermodynamics.

Annila A. The 2nd law of thermodynamics delineates dispersal of energy. Int. Rev. Phys. 2010 4, 29-34. (pdf)
The universal law is given in its diverse forms.

Annila A. All in action. Entropy 2010 12, 2333-2358. (pdf) https://doi:10.3390/e12112333 arxiv.org/abs/1005.3854
Nature in its entirety and every detail is described in terms of quantized actions and related mathematical conjectures are examined.

Annila A, Salthe S. Cultural naturalism. Entropy 2010 12, 1325-1343. (pdf) https://doi:10.3390/e12061325а
Culture is described as a society's means to consume free energy.

Annila A, Salthe S. Physical foundations of evolutionary theory. J. Non-equilb. Thermodyn. 2010 35, 301-321. (pdf) https://doi:10.1515/jnetdy.2010.019
The theory of evolution by natural selection is subsumed by the 2nd law of thermodynamics.

Mäkelä T, Annila A. Natural patterns of energy dispersal. Phys. Life Rev. 2010 7, 477-498. (pdf) https://doi:10.1016/j.plrev.2010.10.001
Many mathematical models of systems are found as approximations of the evolutionary equation of motion.

Annila A. Least-time paths of light. Mon. Not. R. Astron. Soc. 2011 416, 2944-2948. (pdf) https://doi:10.1111/j.1365-2966.2011.19242.x
The principle of least action gives paths of light through space without dark energy and dark matter.

Koskela M, Annila A. Least-action perihelion precession. Mon. Not. R. Astron. Soc. 2011 417, 1742-1746. (pdf) https://doi.org/10.1111/j.1365-2966.2011.19364.x arxiv.org/abs/1009.1571
Perihelion precession is calculated using the principle of least action and ascribed to the gravity of the whole Universe.

Anttila J, Annila A. Natural games. Phys. Lett. A 2011 375, 3755-3761. (pdf) https://doi.org/10.1016/j.physleta.2011.08.056 arxiv.org/abs/1103.1656
Behavior in the context of game theory is described as a natural process.

Hartonen T, Annila A. Natural networks as thermodynamic systems. Complexity 2012 18, 53-62. (pdf) https://doi:10.1002/cplx.21428 arxiv.org/abs/1106.4127
Universal characteristics of networks follow from the least-time free energy consumption.

Annila A, Kallio-Tamminen T. Tangled in entanglement. Physics Essays 2012 25, 495-499. (pdf) https://doi.org/10.48550/arXiv.1006.0463
Conceptual conundrums of quantum mechanics are resolved using the principle of least action.

Annila A. Probing Mach's principle. Mon. Not. R. Astron. Soc. 2012 423, 1973-1977. (pdf) https://doi.org/10.1111/j.1365-2966.2012.21022.x
The principle of least action accounts for geodetic precession and frame-dragging effects by photon-embodied physical vacuum.

Annila A. Space, time and machines. Int. J. Theor. Math. Phys. 2012 2, 16-32. (pdf) sapub.org/10.5923 arxiv:0910.2629
Some present problems in physics and contemporary conjectures of mathematics are addressed by the 2nd law of thermodynamics.

Annila A. The meaning of mass. Int. J. Theor. Math. Phys. 2012 2, 67-78. (pdf) https://doi:10.5923/j.ijtmp.20120204.03
Particles are actions whose quantized geodesics manifest as charges, magnetic moments, and masses.

Pernu TK, Annila A. Natural emergence. Complexity 2012 17, 44-47. (pdf) https://doi:10.1002/cplx.21388а
New qualities will materialize when surrounding quanta incorporate to the system and thereby open up new motional modes.

Koskela M, Annila A. Looking for LUCA. Genes 2012 3, 81-87. (pdf) https://doi.org/10.3390/genes3010081
The unattainable quest for the last universal common ancestor implies impaired understanding of what life actually is.

Annila A, Annila E. The significance of sex. BioSystems 2012 110, 156-161. (pdf) https://doi.org/10.1016/j.biosystems.2012.09.006
Both sexual and asexual reproduction can be regarded merely as a means to consume free energy in least time.

Keto J, Annila A. The capricious character of nature. Life 2012 2, 165-169. (pdf) https://doi.org/10.3390/life2010165
Courses of nature are inherently unpredictable since processes and their driving forces depend on each other.

Annila A. Physical portrayal of computational complexity. ISRN Computational Mathematics 2012 321372, 1-15. (pdf) https://doi.org/10.5402/2012/321372 https://doi.org/10.48550/arXiv.0906.1084
Computation is intractable when there are degrees of freedom for dissipative computational steps.

Annila A, Salthe S. On intractable tracks. Physics Essays 2012 25, 232-237. (pdf)
The principle of least action allows us to understand why nature displays rules and regularities but is nevertheless unpredictable.

Annila A, Salthe S. Threads of time. ISRN Thermodynamics 2012 850957, 1-7. (pdf) https://doi.org/10.5402/2012/850957
The flux of quanta embodies the flow of time, and the irreversible free energy consumption creates time's arrow.

Varpula S, Annila A, Beck C. Thoughts about thinking. Advanced Studies in Biology 2013 5, 135-149. (pdf) http://dx.doi.org/10.12988/asb.2013.13012
A holistic account of the human brain is given by the systemic theory of least-time free energy consumption.

Annila A, Baverstock K. Genes without prominence: a reappraisal of the foundations of biology. J. Roc. Soc. Interface 2014 11, 20131017. (pdf) https://doi.org/10.1098/rsif.2013.1017
Genes are no ends in themselves, but at service of least-time free energy consumption.

Annila A, Kolehmainen E. On the divide between animate and inanimate. J. Sys. Chem. 2015 6, 1-3. (pdf) https://doi.org/10.1186/s13322-015-0008-8
Ubiquitous scale free patterns present convincing evidence that demarcation between animate and inanimate is only imaginary.

Annila A. The substance of gravity. Physics Essays 2015 28, 208-218. (pdf) https://doi.org/10.4006/0836-1398-28.2.208
A local gravitational potential and the universal vacuum embody photons in pairs of no net polarization.

Annila A. Cosmic rays report from the structure of space. Advances in Astronomy 2015 ID 135025, 11 pp. (pdf) https://doi.org/10.1155/2015/135025
Spectral features of rays are related by the least-time principle to energy densities of the photon-embodied vacuum in the expanding Universe.

Annila A. Natural thermodynamics. Physica A 2016 444, 843-852. (pdf) https://doi:10.1016/j.physa.2015.10.105
Universal characteristics and principles are derived from statistical physics considering quantized actions to embody every system.

Annila A. On the character of consciousness. Frontiers in Systems Neuroscience 2016 10, 27. (pdf) https://doi:10.3389/fnsys.2016.00027
Several well-known questions and stances about consciousness are examined and illuminated by statistical physics.

Annila A. Rotation of galaxies within gravity of the Universe. Entropy 2016 18, 191-205. (pdf) https://doi:10.3390/e18050191
The galaxy rotational curve is explained by the principle of least action to result from the overall gravity of the expanding Universe.

Grahn P, Annila A, Kolehmainen E. On the exhaust of EM-drive. AIP Advances 2016 6, 065205. (pdf) https://doi:10.1063/1.4953807
The elusive thrust of an electromagnetic drive is identified by the principle of least action to photons co-propagating out-phase.

Annila A, Baverstock K. Discourse on order vs. disorder. Communicative & Integrative Biology 2016 9, e1187348. (pdf) https://doi:10.1080/19420889.2016.1187348
Increase of disorder, just as order, in any system is merely a consequence of least-time free energy consumption.

Annila A, Kolehmainen E. Atomism revisited. Physics Essays 2016 29, 532-541. (pdf) https://doi:10.4006/0836-1398-29.4.532
The ancient atomism guides one to consider everything to be composed of indivisible entities, known today as quantum of actions.

Annila A. Flyby anomaly via least action. Progress in Physics 2017 13, 92-97. (pdf)
The unexpected velocity changes during spacecraft flybys of Earth are accounted for by the principle of least action.

Annila A. Evolution of the universe by the principle of least action. Physics Essays 2017 30, 248-254. (pdf) https://doi.org/10.4006/0836-1398-30.3.248
Path-dependent and scale-free characteristics of universal evolution are accounted for by the principle of least action.

Koivu-Jolma M, Annila A. Epidemic as a natural process. Mathematical Biosciences 2018 299, 97-102. (pdf) https://doi.org/10.1016/j.mbs.2018.03.012
Epidemic is described as a natural process to account for its capricious courses and overarching consequences.

Grahn P, Annila A, Kolehmainen E. On the carrier of inertia. AIP Advances 2018 8, 035028. (pdf) https://doi:10.1063/1.5020240
Inertia is described as a reaction taken to an action by paired-photon embodied vacuum.

Annila A. The art of abstraction: Comment on "Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems" by F. Kuchling, K. Friston, G. Georgiev, M. Levin. Physics of Life Reviews 2020 33, 119–120. (pdf) https://doi.org/10.1016/j.plrev.2019.11.008
The principle of morphogenesis is spelled out.

Annila A. The matter of time. Entropy 2021 23, 943. (pdf) https://doi:10.3390/e23080943
The photon period is the elemental unit of time; time flows as quanta flow.

Annila A. Statistical physics of evolving systems. Entropy 2021 23, 1590. (pdf) https://doi:10.3390/e23121590
Based on the axiom of everything comprising quanta, all systems evolve toward thermodynamic balance with their surroundings.

Annila A. The fundamental nature of motives. Front. Neurosci. 2022, (pdf) https://doi:10.3389/fnins.2022.806160
The motive forces orient agents to consume free energy in the least time.

Lehmonen L, Annila A. Natural classes and natural classification. In Efficiency in Complex Systems, ed. Georgiev GY, Shokrollahi-Far, M. Springer Nature 2022. (pdf) https://doi:10.1007/978-3-030-69288-9
Natural categorization places objects to classes so that free energy is consumed in the least time.

Annila A. On the origin of universal patterns. In Efficiency in Complex Systems, ed. Georgiev GY, Shokrollahi-Far, M. Springer Nature 2022. (pdf) https://doi:10.1007/978-3-030-69288-9
The ubiquitous patterns follow from the least-time consumption of free energy.

Lehmonen L, Annila A. Baryon breakdown in black hole. Front. Phys. 2022 (pdf) https://doi:10.3389/fphy.2022.954439
A black hole is described as a star annihilating neutrons into photons that jet out as high-energy rays.

Annila A, Wikström M. Dark matter and dark energy denote the gravitation of the expanding universe. Front. Phys. 2022, (pdf) https://doi:10.3389/fphy.2022.995977
The gravitational field extending from the distant dense past to the sparse present accounts for the galaxy rotation and velocity dispersion as well as for the distant supernovae data.

Annila A. Chiral conformity emerges from the least-time free energy consumption. Interface Focus 2023 13, 20220074 (pdf) https://doi:10.1098/rsfs.2022.0074
The flows of energy naturally select standard structures over less-fit functional forms to consume free energy in the least time.

Annila A. Philosophy of thermodynamics. Philos. Trans. R. Soc. A 2023 7, 381(2252):20220281 (pdf) https://doi.org/10.1098/rsta.2022.0281
The holistic worldview based on the atomistic axiom of everything comprising quanta provides a perspective on questions such as what the world is, how we know about it, what the meaning of life is, and how we should live.

Annila A. Neutron star characteristics from the neutron structure. Front. Phys. 2023, (pdf) https://doi:10.3389/fphy.2023.1286802
The neutron structure makes sense of the neutron star density, magnetism, spinning axis, and pulsing transients.

Annila A, Wikström M. Quantum entanglement and classical correlation have the same form. Eur. Phys. J. Plus 2024, (pdf) https://doi:10.1140/epjp/s13360-024-05377-8
Classical correlation explaining the EPR experiment shows that quantum mechanics is an effective theory with well-known interpretational issues rather than a complete and comprehensive physical theory.

Annila A, On the Origin of Cognition. Biol. Theory 2024, (pdf) https://doi:10.1007/s13752-024-00472-6
Any sequence of events, from photon absorption to focused awareness, chemical reactions to collective behavior, or from neuronal avalanches to niche adaptation, is understood as an evolution from one state to another toward thermodynamic balance.

Annila A, Comprehensible dynamics of quanta: from the quantum of action to the 2nd law of thermodynamics. Eur. Phys. J. Plus 140, 28 2025. (pdf) https://doi.org/10.1140/epjp/s13360-025-05970-5
The irreversible evolution in the state space toward thermodynamic balance explains that increasing disorder is not a law of nature itself but a consequence of the law to attain balance with incoherent surroundings in the least time.

Papers in progress: please request by email (arto.annila@helsinki.fi)

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