Related papers: Possible canonical distributions for finite system…
We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and…
We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical…
A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is…
It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…
We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy…
We show that an arbitrary probability distribution can be represented in exponential form. In physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in grand canonical…
Traditionally, it is understood that fluctuations in the equilibrium distribution are not evident in thermodynamic systems of large $N$ (the number of particles in the system) \cite{Huang1}. In this paper we examine the validity of this…
Involvement of the environment is indispensable for establishing the statistical distribution of system. We analyze the statistical distribution of a quantum system coupled strongly with a heat bath. This distribution is determined by…
We show that the zeroth law of thermodynamics holds within an alternative version of nonextensive statistical mechanics based on {\it incomplete probability distribution}. The generalized zeroth law leads to a generalized definition of…
We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. Hence, the configurational subsystem is non-extensive in the sense of Tsallis. One of the consequences of this…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., $q \ne 1$), does {\it not} modify anything to the second principle of thermodynamics, which therefore…