When is a hidden variable theory compatible with quantum mechanics?

This paper is devoted to a study of some of the basic conditions which have to be satisfied by a hidden variable theory in order that it can reproduce the quantum mechanical probabilities. Of course one such condition, which emerges from the important theorem of Bell, is that a hidden variable theory has to be non-local. It is shown that a hidden variable theory is also incompatible with the conventional interpretation of mixed states and the mixing operation in quantum theory. It is therefore concluded that, apart from being non-local, a hidden variable theory would also necessarily violate the usual assumption of quantum theory that the density operator provides an adequate characterization of any ensemble of systems, pure or mixed.     

Irreversibility and dissipation in finite-state automata

Irreversibility and dissipation in finite-state automata (FSA) are considered from a physical-information-theoretic perspective. A quantitative measure for the computational irreversibility of finite automata is introduced, and a fundamental lower bound on the average energy dissipated per state transition is obtained and expressed in terms of FSA irreversibility. The irreversibility measure and energy bound are germane to any realization of a deterministic automaton that faithfully registers abstract FSA states in distinguishable states of a physical system coupled to a thermal environment, and that evolves via a sequence of interactions with an external system holding a physical instantiation of a random input string. The central result, which is shown to follow from quantum dynamics and entropic inequalities alone, can be regarded as a generalization of Landauer?s Principle applicable to FSAs and tailorable to specified automata. Application to a simple FSA is illustrated.     

Is There a Fourth Law for Non-Ergodic Systems That Do Work to Construct Their Expanding Phase Space?

Substantial grounds exist to doubt the universal validity of the Newtonian Paradigm that requires a pre-stated, fixed phase space. Therefore, the Second Law of Thermodynamics, stated only for fixed phase spaces, is also in doubt. The validity of the Newtonian Paradigm may stop at the onset of evolving life. Living cells and organisms are Kantian Wholes that achieve constraint closure, so do thermodynamic work to construct themselves. Evolution constructs an ever-expanding phase space. Thus, we can ask the free energy cost per added degree of freedom. That cost is roughly linear or sublinear in the mass constructed. However, the resulting expansion of the phase space is exponential or even hyperbolic. Thus, the evolving biosphere does thermodynamic work to construct itself into an ever-smaller sub-domain of its ever-expanding phase space at ever less free energy cost per added degree of freedom. The universe is not correspondingly disordered. Entropy, remarkably, really does decrease. A testable implication of this, termed here the Fourth Law of Thermodynamics, is that at constant energy input, the biosphere will construct itself into an ever more localized subregion of its ever-expanding phase space. This is confirmed. The energy input from the sun has been roughly constant for the 4 billion years since life started to evolve. The localization of our current biosphere in its protein phase space is at least 10^–2540. The localization of our biosphere with respect to all possible molecules of CHNOPS comprised of up to 350,000 atoms is also extremely high. The universe has not been correspondingly disordered. Entropy has decreased. The universality of the Second Law fails.     

The Role of Metal Ion Polymerization in Beer's Law Deviations Using Extractive-Colorimetric Procedures

Abstract

In the solvent extraction of metal chelates, the presence of polymerized metal ion in either the aqueous or organic layer, can cause the efficiency of extraction to vary throughout a range of metal ion concentrations. Should an extractive-colorimetric determination be employed, a deviation from Beer's Law can result in addition to other intrinsic causes. In this study, the nature of the deviation solely due to polymerization is demonstrated. The absorbances of the extracted metal complexes in the organic phases which are calculated from the analytically determined metal ion concentrations and molar absorptivities are plotted versus the initial metal ion concentrations for some 2,2′-pyridil-mono-and bis-2? and ?2.6 in the plots of log D vs. log [M(II)]_org. are found. At initial metal ion concentratiolns greater than 6 × 10^?5 M, marked negative deviations from the straight line are observed.