Related papers: Monotonicity and Thermodynamic Limit for Short Ran…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…
The steady state for a system of N particle under the influence of an external field and a Gaussian thermostat and colliding with random "virtual" scatterers can be obtained explicitly in the limit of small field. We show the sequence of…
The principal results of this contribution are the weak and strong limits of maxima of contracted stationary Gaussian random sequences. Due to the random contraction we introduce a modified Berman condition which is sufficient for the weak…
A special kind of quasi-homogeneity occurring in thermodynamic potentials of standard thermodynamics is pointed out. Some formal consequences are also discussed.
The omnipresent disorder in physical systems makes it imperative to investigate its effect on the spatial range of interactions for which system remains thermodynamically extensive. Previously known bounds on the statistical free energy for…
The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we…
We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a…
For fluctuating currents in non-equilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show…
We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity. In the context of anisotropic thermal conduction, this can lead to the…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of…
The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the…
The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium…
We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice…
In the setup of isolated quantum systems, it is proved that the thermodynamic entropy and the diagonal entropy must increase extensively in any nontrivial quantum quench. The extensive increase of the thermodynamic entropy is shown for any…
In this paper, we examine fluctuations of polynomial linear statistics for the Anderson model on $\mathbb{Z}^d$ for any potential with finite moments. We prove that if normalized by the square root of the size of the truncated operator,…
We consider the general problem of quenching an interacting Bose gas from the noninteracting regime to the strong repulsive case described by the Tonks-Girardeau limit, with the initial state being a gaussian ensemble for the bosons. A…
We consider paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models, and show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size…
A microscopic model for thermal excitation of vibrational ground state of a molecule interacting with a condensed medium is developed. The master equation for evolution of occupancies of the vibrational levels is derived. The rate constant…
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive…