Arto Annila, Dr., Prof.       

E-mail: arto.annila(at)

Department of Physics

POB 64 (Gustaf Hällströmin katu 2)

FI-00014 University of Helsinki, Finland                   

Phone: +358 44 2047324



Doctor of Tech., Tech. Phys.,

Helsinki Univ. of Tech, 1991

Civil Engineer, Tech. Phys.,

Helsinki Univ. of Tech., 1988

M.Sc. Biochemistry,

University of Helsinki, 1996






· Why Life Originated?

· A challenge to the genetic interpretation of biology

· A Challenge to the Supremacy of DNA

· Evolution as Described by the Second   Law of Thermodynamics

· 2nd Law in Economic Evolution

· Crude Oil and Social Unrest

· Kvanttimekaniikka ja energiavirta

· A second look at supernovae light: Universe's expansion may be understood without dark energy

· Why is economic growth so popular?

· Thermodynamics and poker

· The P-versus-NP page

· Maailma on yksi




· Natural emergenece

· The meaning of mass

· What is life?

· Theory of biology

· The character of natural law

· Spectrum of cosmic rays



Esitelmiä (Talks in Finnish)

· Ajatuksia ajattelusta

· Mitä on elämä?

· Informaation olemus

· Luonnonlain luonne

· Miksi maailma muuttuu?

· Seksin merkitys?

· Selittävätkö luonnonlait kaiken?



Haastatteluja (Interviews in Finnish)

· Minna Pyykön maailma:

· Tiedeykkönen: Maupertuis ja pienimmän vaikutuksen laki



Kirjoituksia (Writings in Finnish)

· Luonnonlain luonne Tieteessä tapahtuu 2014 32, 20-23.

· Ennustamisen vaikeus Tieteessä tapahtuu 2014 32, 51-52.

Research interests:

Holistic worldview


Nature is rich but not random in its diversity. Also complexity of nature is astounding but not arbitrary. We do recognize rules and regularities that we know as laws of physics and chemistry, or those that we refer to as relations in biology, economics, behavioral and social sciences. Disciplinary canons are not disconnected from each other but relate via ubiquitous characteristics of nature. These are skewed distributions that accumulate along sigmoid growth and decline curves which in turn display mostly as straight lines on log-log plots, i.e., follow power laws.
   These all-embracing commonalities
make no distinction between living and non-living or between microscopic and cosmic, which implies that there is a universal organizing principle. Hence, while an observation could be interpreted by some specific theory, all observations ought to be understood by the same general tenet.


The principle of least action was early on thought of as a powerful way to make sense of various complex phenomena as well as of simple matters. It says that a difference in energy of any kind will level off in least time. The naturalistic tenet assigns energy to everything that exists, and describes all processes as least-time consumption of free energy. The natural principle in the form of an equation of motion reveals that evolution is inherently an intractable, path-dependent process.
   Yet evolution is not a random sequence of events.
Processes as flows of energy will themselves search by variation and select naturally those ways and means, such as species and societies or gadgets and galaxies that will consume free energy in the least time. In this way systems step from one state of symmetry to another by either acquiring or expelling at least one quantum of action. It is the photon, the basic building block of everything. A step down in free energy is an irreversible step forward in time.
  Eventually, when a
system attains equilibrium with its surroundings, no new property will emerge and no old one will vanish. Only at the free energy minimum stasis systemic dynamics is on stable and computable trajectories.  



Science by submerging to specialties supplies us with detailed information whereas by recognizing universalities it provides us with thorough comprehension. Indeed, as our delusions of uniqueness have narrowed, our worldview has widened toward entirety.
   Whatever fallacies still remain will vanish in examinations by the natural principle of least time. As apparent from papers below m
any phenomena, puzzles and paradoxes can be comprehended by this supreme law of nature.

Papers (Directory by big questions)


Sharma V, Annila A. Natural process – Natural selection. Biophys. Chem. 2007 127, 123–128. (pdf) doi:10.1016/j.bpc.2007.01.005

           The principle of increasing entropy as an equation of motion is derived from statistical physics of open systems.

Grönholm T, Annila A. Natural distribution. Math. Biosci. 2007 210, 659–667. (pdf) doi:10.1016/j.mbs.2007.07.004

           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) doi:10.1098/rspa.2008.0178

           The principle of least action is shown as 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) arXiv:0906.0254

           Standards of nature 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 is found to follow from the 2nd law of thermodynamics.

Würtz P, Annila A. Roots of diversity relations. J. Biophys. 2008 (pdf) doi:10.1155/2008/654672. arXiv:0906.0251

           Species-area relationship is 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) doi:10.1017/S1473550408004308

           Life in its entirety is a natural process that follows the 2nd law of thermodynamics.

Tuisku P, Pernu TK, Annila A. In the light of time. Proc. R. Soc. A. 2009 465, 1173–1198. (pdf) doi:10.1098/rspa.2008.0494

           A flow of time is a quantized flow of energy.

Karnani M, Annila A. Gaia again. BioSystems 2009 95, 82–87. (pdf) doi:10.1016/j.biosystems.2008.07.003 

           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)

           Protein folding is an inherently intractable process.

Annila A, Kuismanen E. Natural hierarchy emerges from energy dispersal. BioSystems 2009 95, 227–233. (pdf)

           Hierarchy of nature is a manifestation of the 2nd law of thermodynamics.

Karnani M, Pääkkönen K, Annila A. The physical character of information. Proc. R. Soc. A. 2009 465, 2155–2175. (pdf)

           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) 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)

           Succession 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 2nd law of thermodynamics is given in its diverse forms.

Annila A. All in action. Entropy 2010 12, 2333–2358. (pdf)

           Nature in its entirety and every detail is described in terms of actions and related mathematical conjectures are examined.

Annila A, Salthe S. Cultural naturalism. Entropy 2010 12, 1325–1343. (pdf) doi:10.3390/e12061325 

           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)

           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, 477498. (pdf) doi:10.1016/j.plrev.2010.10.001

           Many mathematical models are found as approximations of the evolutionary equation of motion.

Koskela M, Annila A. Least-action perihelion precession. Mon. Not. R. Astron. Soc. 2011 417, 1742–1746. (pdf)

           Perihelion precession is calculated using the principle of least action.

Annila A. Least-time paths of light. Mon. Not. R. Astron. Soc. 2011 416, 2944–2948. (pdf)

           The principle of least action gives paths of light through space without dark energy and dark matter.

Anttila J, Annila A. Natural games. Phys. Lett. A 2011 375, 37553761. (pdf)

           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, 5362. (pdf)

           Scale-free characteristics of networks follow from the least-time energy dispersal.

Annila A, Kallio-Tamminen T. Tangled in entanglement. Physics Essays 2012 25, 495499. (pdf)

           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, 19731977. (pdf)

           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) 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)

           Particles are described as actions to explain that charges, magnetic moments and masses are manifestations of quantized geodesics.

Pernu TK, Annila A. Natural emergence. Complexity 2012 17, 4447. (pdf) doi:10.1002/cplx.21388 

           Novel qualities will materialize when quanta from surroundings incorporate into a system and thereby open up new modes of interactions.

Koskela M, Annila A. Looking for LUCA. Genes 2012 3, 8187. (pdf)

           The quest for the last universal common ancestor is an unattainable attempt that indicates impaired understanding of what life actually is.

Annila A, Annila E. The significance of sex. BioSystems 2012 110, 156161. (pdf

           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, 165169. (pdf)

           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, 115. (pdf) 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, 232237. (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, 17. (pdf)

           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, 135149. (pdf)

           A holistic account of the human brain is given by the 2nd law of thermodynamics.

Annila A, Baverstock K. Genes without prominence: a reappraisal of the foundations of biology. J. Roc. Soc. Interface 2014 11, 20131017. (pdf)

           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 . (pdf)

           Ubiquitous scale free patterns present convincing evidence that demarcation between animate and inanimate is only imaginary.

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