1 INFINITE ENERGY • ISSUE 102 • MARCH/APRIL 2012 Abstract This paper reports explorations into the scientific principles of, and ramifications from, the coupling of solute-concen- tration fluctuations to an external field. Solute-concentra- tion fluctuations are a variety of spontaneous particle fluc- tuations—random vacillations in the distribution of solute particles within solute-solvent solutions—that have long been known to exist. In the study presented here, it is posit- ed that the fluctuations are also exotic solute species that develop gravitational potential energy within liquid solu- tions that are at rest within earth’s gravity. To test this hypothesis, experimental results from analytical electro- chemistry, using simple two-electrode gravity cells (Au- AuCl 3 -Au) with 0.5 molar aqueous auric chloride elec- trolytes, were compared against numerical expectations developed from statistical mechanics. The salient technical findings are these: The gravitational potential energies of solute-concentration fluctuations exist in accord with theo- retical modeling and calculations; they (1) add to the chem- ical potential of a solute in solution, (2) participate in the equilibrium equation and (3) preclude the electrochemical cells from a steady state of equilibrium. 1. Introduction/Overview 1.1 — The Second Law and Particle Fluctuation Thermodynamic Equilibrium: In simple fluid systems—gases and liquids—thermodynamic equilibrium has two facets. Static equilibrium occurs at the macroscopic level; a fluid’s energies are balanced and latent, and so its measureable properties cannot spontaneously change. In this condition a system can only be passive and inanimate. Dynamic equilib- rium exists at the microscopic level of atoms and molecules where the fluid is constantly in flux due to the particles' incessant and random motions. But these spontaneous par- ticle fluctuations are small in magnitude and brief in exis- tence, and they offset or balance one another; microscale particle fluctuations do not alter the equilibrium properties of the macroscopic system. The tendency for all material sys- tems to devolve to a state of thermodynamic equilibrium is omnipresent, heedless of the size, composition or complexi- ty of a system, and is one of the statements of the second law of thermodynamics. Solute-Concentration Fluctuation: Within a liquid solute-sol- vent solution—a volume of saltwater, for instance—a solute- concentration fluctuation is both a stochastic reaction and an ephemeral object. In the first instance it is merely a chance clustering of solute particles that haphazardly aggre- gate and then disperse. In the second, it is a subvolume with- in the bulk fluid that briefly contains more or fewer solute particles than its surroundings; the precise value being always in flux due to the ceaseless random movements of the particles themselves. 1 In all solutions a solute is different than the solvent, and so fluctuated subvolumes are transito- ry cloud-like objects with distinct properties of their own: solute concentration, mass density, magnetic susceptibility. These properties are significant because they distinguish the fluctuated subvolumes from the surrounding bulk fluid. 2 These fluctuated subvolumes are the solute-concentration fluctuations that are the focus of study in this paper. Spontaneous particle fluctuation is not a new concept in physics. It started with the idea that matter is made of atoms that are always in random motion, and it became a corner- stone in the kinetic theory of gases that was established in the 19th century. Since 1905, from theoretical studies by Einstein and by Smoluchowski in combination with the 1907-1908 experimental confirmation of their calculations by Perrin (dealing with the erratic movement—Brownian motion—of particulate suspended in fluids), particle fluctu- Testing the Definition of Thermodynamic Equilibrium Part 1: Systems in a Gravitational Field Norman K. Borsuk* Thermodynamic equilibrium in a liquid solution is a balancing of the steady-state potential energies that play on the chemical species—the solvent and solutes—within the macroscopic system. In prac- tice, a relatively simple equilibrium equation is the balance beam that mathematically equilibrates the components’ energies and makes it possible to define and predict a solution’s equilibrium properties that, ultimately, can be tested in actual experiment. An equilibrium equation’s efficacy is dependent, in no small part, on underlying models, theories and laws that prescribe which quantities enter the formula in the first place. Failure to include a relevant energy or chemical component can lead to incomplete and misleading definitions, erroneous predictions and, when the oversight is corrected and all is set straight again, possibly to revision or replacement of fundamental canon. Such is the impact of solute-concentration fluctuations and their gravitational potential energies on equilibrium theory and the second law of thermodynamics.