Related papers: Finite thermal reservoirs and the canonical distri…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
We study the configurational probability distribution of a mono-atomic gas with a finite number of particles N in the micro-canonical ensemble. We give two arguments why the thermodynamic entropy of the configurational subsystem involves…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this "nanothermodynamics," and stress how it also applies to large systems that subdivide…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
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…
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…
Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. However, some 150 years ago the original motivation of thermodynamics was the description of steam engines, i.e. boiling water. Its essential…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
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…
Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic…
It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. (Only in this case this is equivalent to the fundamental microcanonical ensemble.) However, some 170 years ago the original motivation of…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…