Related papers: Some interesting observations on the free energy p…
We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $S\geq 1/2$. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas…
Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design…
Free electron approximation for electron states in poly($p$-phenylene vinylene) and other conjugated systems is developed. It provides simple and clear analytical expressions for energies of electron states and for wave functions. The…
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
The evaluation of the free energy of a stochastic model is considered a significant issue in various fields of physics and machine learning. However, the exact free energy evaluation is computationally infeasible because the free energy…
Maximizing the amount of work harvested from an environment is important for a wide variety of biological and technological processes, from energy-harvesting processes such as photosynthesisto energy storage systems such as fuels and…
One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is…
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit…
We argue that the concepts of "freedom of choice" and of "causal order" are intrinsically linked: a choice is considered "free" if it is correlated only to variables in its causal future. We discuss the implications of this to Bell-type…
Recent cosmological observations suggest that the dark energy equation of state may have changed in the latter stages of cosmic history. We introduce a quintessence scenario, termed bounded dark energy, capable of explaining this feature in…
A recent result, relating the (irreversible) work performed on a system during a non-quasistatic process, to the Helmholtz free energy difference between two equilibrium states of the system, is discussed. A proof of this result is given…
Starting for the Stillinger and Weber expression for the free energy of supercooled liquids, we extend the free energy to the case in which two time scales separate and the system is in quasi-equilibrium. The concept of an effective…
Recent theoretical predictions and experimental measurements have demonstrated that equilibrium free energy differences can be obtained from exponential averages of nonequilibrium work values. These results are similar in structure, but not…
Interface free energy is the contribution to the free energy of a system due to the presence of an interface separating two coexisting phases at equilibrium. It is also called surface tension. The content of the paper is 1) the definition…
We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti-Sommers representation of the…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
An approach to implementing variational Bayesian inference in biological systems is considered, under which the thermodynamic free energy of a system directly encodes its variational free energy. In the case of the brain, this assumption…
We study the behaviour of free energies of baryonic systems composed of three heavy quarks on the lattice in SU(3) pure gauge theory at finite temperature. For all temperatures above $T_c$ we find that the connected part of the singlet…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be…