Related papers: Finding Exact Forms on Thermodynamic Manifolds
It is by now well-known that ground states of gapped one-dimensional (1d) quantum-many body systems with short-range interactions can be studied efficiently using classical computers and matrix product state techniques. A corresponding…
The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional flat spacetime is analyzed. Inside the ring the spacetime is flat, whereas outside it is conical flat. The first law of thermodynamics applied to the…
We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases,…
Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
A description of thermodynamics for continuum mechanical systems is presented in the coordinate-free language of exterior calculus. First, a careful description of the mathematical tools that are needed to formulate the relevant…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is…
This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
Thermal duality, which relates the physics of closed strings at temperature T to the physics at the inverse temperature 1/T, is one of the most intriguing features of string thermodynamics. Unfortunately, the classical definitions of…
Based on a rigorous thermodynamic framework, this work develops a two-fluid magnetohydrodynamic model grounded in the Helmholtz free energy formalism. The model maintains full thermodynamic consistency by simultaneously satisfying energy…
In the contact-geometric formulation of classical thermodynamics distinction is made between the energy and entropy representation, which can be resolved by taking homogeneous coordinates for the intensive variables. This results in a…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
Systems at finite temperature make up the vast majority of realistic physical scenarios. Indeed, although zero temperature is often accompanied by simpler mathematics, the richness in physical results is evident when one considers the…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…