相关论文: Optimal Selection of Structural Degree of Freedoms…

We obtain the squeezed coherent states (SCS) for a free particle with exponentially time-varying mass. We write these states in terms of the squeeze and displacement parameters on the time-independent Fock states. Thus, we find a condition…

Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated.…

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "macrostates" (e.g. sets of "microstates"), the consequence on…

An ideal Maxwell-Boltzmann gas confined in various rectangular nano domains is considered under quantum size effects. Thermodynamic quantities are calculated from their relations with partition function which consists of triple infinite…

We study the time evolution of the Boltzmann entropy of a microstate during the non-equilibrium free expansion of a one-dimensional quantum ideal gas. This quantum Boltzmann entropy, $S_B$, essentially counts the "number" of independent…

In contrast to equilibrium systems, non-equilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber and heat bath rates, we illustrate this expectation for an Ising lattice…

We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control…

The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…

To illustrate Boltzmann's construction of an entropy function that is defined for a microstate of a macroscopic system, we present here the simple example of the free expansion of a one dimensional gas of non-interacting point particles.…

We show by microscopic calculation that thermodynamics of the multicomponent Sutherland model is equivalent to that of a free particle system with fractional exclusion statistics at all temperatures. The parameters for exclusion statistics…

We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Ma\~n\'e, establishing existence and uniqueness of equilibrium states for natural classes of potential functions. In particular, we…

We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in…

This paper introduces the notion of state constraints for optimal control problems governed by fractional elliptic PDEs of order $s \in (0,1)$. There are several mathematical tools that are developed during the process to study this…

This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schr\"odinger equation allows to construct quantum trajectories describing the dynamics of the system…

The microstate of any degree of freedom of any classical dynamical system can be represented by a point in its two dimensional phase space. Since infinitely precise measurements are impossible, a measurement can, at best, constrain the…

Exact and approximate expressions for thermodynamic characteristics of heated matter, which consists of particles with finite mass-widths, are constructed. They are expressed in terms of Fermi/Bose distributions and spectral functions,…

The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…

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…

Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…

Individual phases are commonly considered as the building blocks of materials. However, the accurate theoretical prediction of properties of individual phases remains elusive. The top-down approach by decoding genomic building blocks of…