1. The Physics of Information 2 2. Thermodynamics 2 2.1. The laws 3 2.2. Free energy 6 3. Statistical mechanics 7 3.1. Definitions and postulates 8 3.2. A simple model system of magnetic spins 9 3.3. The Maxwell-Boltzmann distribution 10 3.4. Free energy revisited 11 3.5. Gibbs entropy 12 4. Nonlinear dynamics 12 4.1. The ergodic hypothesis 13 4.2. Chaos and limits to prediction 14 4.3. Quantif...

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka’s expectation propagation. Lastly, we derive a sparse representation version of the sequential algorithm. The usefulness of the app...

A simple expression for the Gibbs free energy of formation of a pure component or a eutectic alloy glass, relative to the stable crystalline phase (or phases) at the same temperature is deduced by use of thermodynamic arguments. The expression obtained is supposed to apply to both monocomponent and multicomponent liquid alloys that might become glasses from the supercooled liquid state, irrespe...

The sequential changes occurring with cancer progression are now being harnessed with therapeutic intent. Yet, there is no understanding of the chemical thermodynamics of proteomic changes associated with cancer progression/ cancer stage. This manuscript reveals a strong correlation of a chemical thermodynamic measure (known as Gibbs free energy) of protein-protein interaction networks for seve...

Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization resu...

Noyes [Noyes, R. M. (1981) Proc. Natl. Acad. Sci. USA 78, 7248-7249] has obtained a result for the Gibbs free energy per unit mass in a continuous flow stirred tank reactor, which states that the steady-state free energy increases monotonically with decreasing residence time for any stable stationary point. We show that his derivation is based on an erroneous stability criterion. We further inv...

Modeling and optimization of synthesis gas production via the non-catalytic partial oxidation of methane (NCPO) were studied by minimizing of Gibbs free energy, and comparison studies were carried out to analyze the mechanism of syngas production. For this purpose, concentrations of CO2 and H2O in the feed were optimized in specified pressure and temperature, such that the hydrogen to carbon mo...

palladium (ii) coordination complexes catalyze the reaction of alcohols with ketones to yield ethers. during the catalytic cycle, the alcohol adds selectively to the β-carbon (anti-markovnikov). in this work, mechanism and kinetics for the reaction of methanol with methyl vinyl ketone (mvk), being catalyzed by pd, has been theoretically investigated in detail. using quantum mechanical approach,...