Related papers: Particle in a box at high temperature
For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic…
A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the…
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…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
We study the non-equilibrium thermodynamics of a single particle with two available energy levels, in contact with a classical (Maxwell-Boltzmann) or quantum (Bose-Einstein) heat bath. The particle can undergo transitions between the levels…
We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
Classical thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a…
A recent description of an exact map for the equilibrium structure and thermodynamics of a quantum system onto a corresponding classical system is summarized. Approximate implementations are constructed by pinning exact limits (ideal gas,…
We consider a system of particles confined in a box $\La\subset\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low…
We consider a system of $N$ particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding…
Controlling interactions out of thermodynamic equilibrium is crucial for designing addressable and functional self-organizing structures. These active interactions also underpin collective behavior in biological systems. Here we study a…
Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson…
These days, as high energy particle colliders become unavailable for testing speculative theoretical ideas, physicists are looking to other environments that may provide extreme conditions where theory confronts physical reality. One such…
Temperature in a simple thermodynamical system is not limited from above. It is also widely believed that it does not make sense talking about temperatures higher than the Planck temperature in the absence of the full theory of quantum…
These days, as high energy particle colliders become unavailable for testing speculative theoretical ideas, physicists are looking to other environments that may provide extreme conditions where theory confronts physical reality. One such…
The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
These days, as high energy particle colliders become unavailable for testing speculative theoretical ideas, physicists are looking to other environments that may provide extreme conditions where theory confronts physical reality. One such…
In the preceding paper, the structure and thermodynamics of a given quantum system was represented by a corresponding classical system having an effective temperature, local chemical potential, and pair potential. Here, that formal…