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Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…
The goal of the paper is to derive a revised condition of global equilibrium in complex chemical systems as variational principle in formalism of recently developed discrete thermodynamics (DTD) of chemical equilibria. In classical approach…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to H\"older-continuous real-valued potentials. The construction of equilibrium states associated to matrix-valued potentials is much more…
We consider the canonical ensemble of a system of point particles on the sphere interacting via a logarithmic pair potential. In this setting, we study the associated Gibbs measure and partition function, and we derive explicit formulas…
In this paper, we suppose a possible extension of Gibbs ensemble theory so that it can provide a reasonable description to phase transitions and spontaneous symmetry breaking. The extension is founded on three hypotheses, and can be…
In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized $\mathrm{U}$-statistic and with a general base measure. Expressing the asymptotic free energy as an optimization problem over a space of…
Classical phase transitions, like solid-liquid-gas or order-disorder spin magnetic phases, are all driven by thermal energy fluctuations by varying the temperature. On the other hand, quantum phase transitions happen at absolute zero…
In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the autors [1], which takes into account nonlinear effects, the role of the cubic in concentration…
Gibbs states are a natural model of quantum matter at thermal equilibrium. We investigate the role of external fields in shaping the entanglement structure and computational complexity of high-temperature Gibbs states. External fields can…
We generalize the thermal pure quantum (TPQ) formulation of statistical mechanics, in such a way that it is applicable to systems whose Hilbert space is infinite dimensional. Assuming particle systems, we construct the grand-canonical TPQ…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold…
We formulate two estimation problems for pipeline systems in which measurements of compressible gas flow through a network of pipes is affected by time-varying injections, withdrawals, and compression. We consider a state estimation problem…
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is…
Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called…
Using the "Liouville space'' (the space of operators) of the massive Ising model of quantum field theory, there is a natural definition of form factors in any mixed state. These generalize the usual form factors, and are building blocks for…
We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by…
The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…
For realistic crystals, the free energy strictly formulated in ensemble theory can hardly be obtained because of the difficulty in solving the high-dimension integral of the partition function, the dilemma of which makes it even a doubt if…