Why did life emerge?

Many mechanisms, functions and structures of life have been unraveled. However, the fundamental driving force that propelled chemical evolution and led to life has remained obscure. The second law of thermodynamics, written as an equation of motion, reveals that elemental abiotic matter evolves from the equilibrium via chemical reactions that couple to external energy towards complex biotic non-equilibrium systems. Each time a new mechanism of energy transduction emerges, e.g., by random variation in syntheses, evolution prompts by punctuation and settles to a stasis when the accessed free energy has been consumed. The evolutionary course towards an increasingly larger energy transduction system accumulates a diversity of energy transduction mechanisms, i.e. species. The rate of entropy increase is identified as the fitness criterion among the diverse mechanisms, which places the theory of evolution by natural selection on the fundamental thermodynamic principle with no demarcation line between inanimate and animate

In the light of time

The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic

Physical portrayal of computational complexity

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized to complete in non-polynomial time (NP). The irreversible process with three or more degrees of freedom is found intractable because, in terms of physics, flows of energy are inseparable from their driving forces. In computational terms, when solving problems in the class NP, decisions will affect subsequently available sets of decisions. The state space of a non-deterministic finite automaton is evolving due to the computation itself hence it cannot be efficiently contracted using a deterministic finite automaton that will arrive at a solution in super-polynomial time. The solution of the NP problem itself is verifiable in polynomial time (P) because the corresponding state is stationary. Likewise the class P set of states does not depend on computational history hence it can be efficiently contracted to the accepting state by a deterministic sequence of dissipative transformations. Thus it is concluded that the class P set of states is inherently smaller than the set of class NP. Since the computational time to contract a given set is proportional to dissipation, the computational complexity class P is a subset of NP.Comment: 16, pages, 7 figure

Natural process – Natural selection

Life is supported by a myriad of chemical reactions. To describe the overall process we have formulated entropy for an open system undergoing chemical reactions. The entropy formula allows us to recognize various ways for the system to move towards more probable states. These correspond to the basic processes of life i.e. proliferation, differentiation, expansion, energy intake, adaptation and maturation. We propose that the rate of entropy production by various mechanisms is the fitness criterion of natural selection. The quest for more probable states results in organization of matter in functional hierarchies

Probing Mach's principle

The principle of least action in its original form \'a la Maupertuis is used to explain geodetic and frame-dragging precessions which are customarily accounted for a curved spacetime by general relativity. The obtained least-time equations of motion agree with observations and are also in concert with general relativity. Yet according to the least-time principle, gravitation does not relate to the mathematical metric of spacetime, but to a tangible energy density embodied by photons. The density of free space is in balance with the total mass of the Universe in accord with Planck's law. Likewise, a local photon density and its phase distribution are in balance with mass and charge distribution of a local body. Here gravitational force is understood as an energy density difference that will diminish when the oppositely polarized pairs of photons co-propagate from the energy-dense system of bodies to the energy-sparse system of the surrounding free space. Thus when the body changes its state of motion, the surrounding energy density must accommodate the change. The concurrent resistance in restructuring of the surroundings, ultimately involving the entire Universe, is known as inertia. The all-around propagating energy density couples everything with everything else in accord with Mach's principle.Comment: 7 pages, to appear in MNRA