Publication

Large Deviations and Free Energy of Gibbs Measure for the Dynamical Φ3-Model in Infinite Volume

2026

Abstract

We study the large deviations for focusing Gibbs measures by analyzing the asymptotic behavior of the free energy in the infinite volume limit. This is the invariant Gibbs measure for the dynamical Φ32-models. From our sharp estimates for the partition function, we establish a concentration phenomenon of the Φ32-measure around the zero field, leading to a triviality result in the infinite volume: the ensemble collapses onto a delta function on the zero field.

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2026

Abstract

Official source

Related concepts (32)

Gibbs measure

In mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics. It is a generalization of the canonical ensemble to infinite systems. The canonical ensemble gives the probability of the system X being in state x (equivalently, of the random variable X having value x) as Here, E is a function from the space of states to the real numbers; in physics applications, E(x) is interpreted as the energy of the configuration x.

Gibbs free energy

In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy.

Helmholtz free energy

In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.

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