RESUMEN
Increasing interest in the thermodynamics of small and/or isolated systems, in combination with recent observations of negative temperatures of atoms in ultracold optical lattices, has stimulated the need for estimating the conventional, canonical temperature Tcconv of systems in equilibrium with heat baths using eigenstate-specific temperatures (ESTs). Four distinct ESTs-continuous canonical, discrete canonical, continuous microcanonical, and discrete microcanonical-are accordingly derived for two-level paramagnetic spin lattices (PSLs) in external magnetic fields. At large N, the four ESTs are intensive, equal to Tcconv, and obey all four laws of thermodynamics. In contrast, for N < 1000, the ESTs of most PSL eigenstates are non-intensive, differ from Tcconv, and violate each of the thermodynamic laws. Hence, in spite of their similarities to Tcconv at large N, the ESTs are not true thermodynamic temperatures. Even so, each of the ESTs manifests a unique functional dependence on energy which clearly specifies the magnitude and direction of their deviation from Tcconv; the ESTs are thus good temperature estimators for small PSLs. The thermodynamic uncertainty relation is obeyed only by the ESTs of small canonical PSLs; it is violated by large canonical PSLs and by microcanonical PSLs of any size. The ESTs of population-inverted eigenstates are negative (positive) when calculated using Boltzmann (Gibbs) entropies; the thermodynamic implications of these entropically induced differences in sign are discussed in light of adiabatic invariance of the entropies. Potential applications of the four ESTs to nanothermometers and to systems with long-range interactions are discussed.
RESUMEN
Immunoassays are important tools for the rapid detection and identification of pathogens, both clinically and in the research laboratory. An immunoassay with the potential for the detection of influenza was developed and tested using hemagglutinin (HA), a commonly studied glycoprotein found on the surface of influenza virions. Gold nanoparticles were synthesized, which present multiple peptide epitopes, including the HA epitope, in order to increase the gravimetric response achieved with the use of a QCM immunosensor for influenza. Specifically, epitopes associated with HA and FLAG peptides were affixed to gold nanoparticles by a six-mer PEG spacer between the epitope and the terminal cysteine. The PEG spacer was shown to enhance the probability for interaction with antibodies by increasing the distance the epitope extends from the gold surface. These nanoparticles were characterized using thermogravimetric analysis, transmission electron microscopy, matrix-assisted laser desorption/ionization-time of flight, and (1)H nuclear magnetic resonance analysis. Anti-FLAG and anti-HA antibodies were adhered to the surface of a QCM, and the response of each antibody upon exposure to HA, FLAG, and dual functionalized nanoparticles was compared with binding of Au-tiopronin nanoparticles and H5 HA proteins from influenza virus (H5N1). Results demonstrate that the immunoassay was capable of differentiating between nanoparticles presenting orthogonal epitopes in real-time with minimal nonspecific binding. The detection of H5 HA protein demonstrates the logical extension of using these nanoparticle mimics as a safe positive control in the detection of influenza, making this a vital step in improving influenza detection methodology.