Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.Comment: 5 page

Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Chemical Reactions

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and re-verse fluxes and free energy for any chemical process operating in a steady state. This rela-tionship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.Comment: 11 page

Data Unfolding with Wiener-SVD Method

Data unfolding is a common analysis technique used in HEP data analysis. Inspired by the deconvolution technique in the digital signal processing, a new unfolding technique based on the SVD technique and the well-known Wiener filter is introduced. The Wiener-SVD unfolding approach achieves the unfolding by maximizing the signal to noise ratios in the effective frequency domain given expectations of signal and noise and is free from regularization parameter. Through a couple examples, the pros and cons of the Wiener-SVD approach as well as the nature of the unfolded results are discussed.Comment: 26 pages, 12 figures, match the accepted version by JINS

Shifting the Quantum-Classical Boundary: Theory and Experiment for Statistically Classical Optical Fields

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schr\"odinger's famous remark about it [Proc. Camb. Phil. Soc. 31, 555 (1935)], prompts examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments, and report here values of the Bell parameter greater than ${\cal B} = 2.54$. This is many standard deviations outside the limit ${\cal B} = 2$ established by the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [Phys. Rev. Lett. 23, 880 (1969)], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit ${\cal B} = 2.828...$. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.Comment: Comments and Remarks are warmly welcome! arXiv admin note: text overlap with arXiv:1406.333