Related papers: The Canonical Ensemble and the Central Limit Theor…

For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes…

The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability…

There is a consensus in science that information theory and statistical physics have a close relationship but the literary proofs of the equivalence between most of the conceptions in the two disciplines are still missing. In this work,…

The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out…

We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the…

We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle's libraries for analysis and measure-theoretic probability. The proof of…

We consider the canonical ensemble of $N$ particles admitting a strange Hamiltonian description. Each of the particles obeys a set of Newtonian equation of motion, which can also be described by the standard canonical Hamiltonian mechanics.…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

We consider N bosons occupying a discrete set of single-particle quantum states in an isolated trap. Usually, for a given excitation energy, there are many combinations of exciting different number of particles from the ground state,…

Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…

We show how the Legendre transforms of the fundamental thermodynamic relation can be used to introduce different statistical ensembles.

In this paper, we study the physics of mesoscopic systems with noninteracting, but fixed number of electrons. From a technical point of view, this means a discussion of the differences between the canonical and the grand canonical ensemble…

We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori…

A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and…

We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…

The different interpretations of quantum mechanics yield the same experimental results, which may give the impression that the question of what interpretation is the true one, is a philosophical question, not a scientific one. But in this…

Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…