Related papers: Statistical entropy of quantum systems
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the…
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
This paper is an introduction to the von Neumann entropy in a historic approach. Von Neumann's gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. In the analysis of his ideas we…
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in…
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…
We present a scheme to evaluate thermodynamic variables for a system coupled to a heat bath under a time-dependent external force using the quasi-static Helmholtz energy from the numerically "exact" hierarchical equations of motion (HEOM).…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
We introduce an ergotropy-based formulation of quantum thermodynamics, which provides a strong connection between average heat and von Neumann entropy. By adopting this formulation, we can reinterpret the infinitesimal average heat in terms…
Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…
An attempt toward the operational formulation of quantum thermodynamics is made by employing the recently proposed operations forming positive operator-valued measures for generating thermodynamic processes. The quantity of heat as well as…
The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it.…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
Despite well over a century of effort, the proper expression for the classical entropy in statistical mechanics remains a subject of debate. The Boltzmann entropy (calculated from a surface in phase space) has been criticized as not being…
We study the entropy of small subsystems in thermalizing quantum many-body systems governed by local Hamiltonians. Assuming the eigenstate thermalization hypothesis, we derive an analytical formula for the von Neumann entropy of…