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A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
The equilibrium state of a system consisting of a large number of strongly interacting electrons can be characterized by its density operator. This gives a direct access to the ground-state energy or, at finite temperatures, to the free…
In this paper, we provide a graphic formulation of non-isothermal reaction systems and show that a non-isothermal detailed balanced network system converges (locally) asymptotically to the unique equilibrium within the invariant manifold…
The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global re-organization. We introduce a measure of…
The presented paper is an attempt to investigate the dynamical states of an hydrodynamical isothermal turbulent self-gravitating system using some powerful tools of the classical thermodynamics. Our main assumption, inspired by the work of…
The time evolution of an extended quantum system can be theoretically described in terms of the Schwinger-Keldysh functional integral formalism, whose action conveniently encodes the information about the dynamics. We show here that the…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…
A system of $N$ particles in a chemical medium in $\mathbb{R}^{d}$ is studied in a discrete time setting. Underlying interacting particle system in continuous time can be expressed as \begin{eqnarray} dX_{i}(t) &=&[-(I-A)X_{i}(t) +…
A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free energy functions.…
By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies and information with their reservoirs through quantum…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with $N$ species, $M$ reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical…
We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…
In previous study [1], we proposed a new physical law applicable to both particle and thermodynamical systems. Additionally, we introduced a physical definition of chaos and self-organization. In the present work, we extend this novel…
The generalized Gibbs-Duhem equation is obtained for systems with long-range interactions in $d$ spatial dimensions. We consider that particles in the system interact through a slowly decaying pair potential of the form $1/r^\nu$ with…