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

Solar Rights and Restrictive Covenants: A Microeconomic Analysis

This comment addresses the enforceability of restrictive covenants in relation to solar energy rights. Articulating the framework for development of solar energy, this comment works through an economic model formulated by Professors Ellickson, Coase, Calabresi, and Malemed. Looking for an efficient allocation of resources, this comment proposes a modernization of common law property principles to ensure the proper growth of solar energy

Natural games

Behavior in the context of game theory is described as a natural process that follows the 2nd law of thermodynamics. The rate of entropy increase as the payoff function is derived from statistical physics of open systems. The thermodynamic formalism relates everything in terms of energy and describes various ways to consume free energy. This allows us to associate game theoretical models of behavior to physical reality. Ultimately behavior is viewed as a physical process where flows of energy naturally select ways to consume free energy as soon as possible. This natural process is, according to the profound thermodynamic principle, equivalent to entropy increase in the least time. However, the physical portrayal of behavior does not imply determinism. On the contrary, evolutionary equation for open systems reveals that when there are three or more degrees of freedom for behavior, the course of a game is inherently unpredictable in detail because each move affects motives of moves in the future. Eventually, when no moves are found to consume more free energy, the extensive-form game has arrived at a solution concept that satisfies the minimax theorem. The equilibrium is Lyapunov-stable against variation in behavior within strategies but will be perturbed by a new strategy that will draw even more surrounding resources to the game. Entropy as the payoff function also clarifies motives of collaboration and subjective nature of decision making.Comment: 14 pages, 1 figur

Space, time and machines

The 2nd law of thermodynamics is used to shed light on present-day puzzles in cosmology. The universal law, given as an equation of motion, describes diverse systems when consuming free energy via various mechanisms to attain stationary states in their respective surroundings. Expansion of the Universe, galactic rotation and lensing as well as clustering of red-shifted spectral lines are found as natural consequences of the maximal energy dispersal that satisfies the conservation of energy, in the forms of kinetic, potential and dissipation. The Universe in its entirety is pictured as a giant Riemann resonator in evolution via step-by-step spontaneous breaking of one stationary-state symmetry to another to diminish energy density differences relative to its zero-density "surroundings". The continuum equation of evolution is proven equivalent to the Navier-Stokes equation. The ubiquitous flow equation has no solution because the forces and flows are inseparable when the dissipative process has three or more degrees of freedom. Since an evolving system is without a norm, there is no unitary transformation to solve the characteristic equation, but detailed trajectories remain inherently intractable. Conversely, stationary-state trajectories can be solved.Comment: 19 pages, 8 figure

Cause of Chirality Consensus

Biological macromolecules, proteins and nucleic acids are composed exclusively of chirally pure monomers. The chirality consensus appears vital for life and it has even been considered as a prerequisite of life. However the primary cause for the ubiquitous handedness has remained obscure. We propose that the chirality consensus is a kinetic consequence that follows from the principle of increasing entropy, i.e. the 2nd law of thermodynamics. Entropy increases when an open system evolves by decreasing gradients in free energy with more and more efficient mechanisms of energy transduction. The rate of entropy increase is the universal fitness criterion of natural selection that favors diverse functional molecules and drives the system to the chirality consensus to attain and maintain high-entropy non-equilibrium states.Comment: 8 pages, 2 figure

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