Related papers: Zeros of the partition function and phase transiti…
Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…
In this work we propose a simple example of a one-dimensional thermodynamic system where non-interacting particles are allowed to move over the $[0,1]$ interval, which are influenced by a potential with a fractal structure. We prove that…
We characterize the breaking of analyticity with respect to the replica number which occurs in random energy models via the complex zeros of the moment of the partition function. We perturbatively evaluate the zeros in the vicinity of the…
We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its…
We use gauge/gravity duality to study the thermodynamics of a generic almost conformal theory, specified by its beta function. Three different phases are identified, a high temperature phase of massless partons, an intermediate…
Starting from the canonical ensemble over the space of pure quantum states, we obtain an integral representation for the partition function. This is used to calculate the magnetisation of a system of N spin-1/2 particles. The results…
We have considered a model of a small finite system with internal particles and surface degrees of freedom. All the main statistical distributions were explicitly obtained, on a pre thermodynamic limit basis. The concept of temperature or…
The thermodynamics of an ideal gas enclosed in a box of volume a1 x a2 x a3 at temperature T is considered. The canonical partition function of the system is expressed in terms of complete elliptic integrals of the first kind, whose…
We systematically explore and show the existence of finite-temperature continuous quantum phase transition (CTQPT) at a critical point, namely, during solidification or melting such that the first-order thermal phase transition is a special…
We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature~(Ostilli and Presilla 2021 \textit{J.…
Phase Transition is associated with a drastic change in some observable (ordered parameter) of the system when the controlled parameter is tuned smoothly. Lee-Yang theory of phase transition is discussed which is related to the accumulation…
The variational theory of equilibrium boson system state to have been previously developed by the author under the density matrix formalism is applicable for researching equilibrium states and thermodynamic properties of the quantum Bose…
Many zero temperature transitions, involving the deviation in the value of a $U(1)$ conserved charge from a quantized value, are described by the dilute Bose gas quantum critical point. On such transitions, we study the consequences of…
The grand canonical thermodynamics of a bosonic system is studied in order to identify the footprint of its own high-density quantum phase transition. The phases displayed by the system at zero temperature establish recognizable patterns at…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
In this study, internal energy (U), electric field (E) and particle number (N) which specify the system quantities i.e. thermodynamical quantities for the proteins. In the frame of thermodynamical formalism, the relation between the heat…
The method to calculate the grand partition function of a particle system, in which constituents interact with each other via potential, that include repulsive and attractive components, is proposed. The cell model, which was introduced to…
The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a…
Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However,…
In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the…