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The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of…
Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the…
In economics, construction of perfect models in a way that would be comparable to the standards customary in physical sciences is generally not feasible. In particular, the observed value for an economic equilibrium may deviate…
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.…
We reconsider the Boltzmann-Gibbs statistical ensemble in thermodynamics using the multinomial coefficient approach. We show that an ensemble is defined by the determination of four statistical quantities, the element probabilities $p_i$,…
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
The role of the algebraic method has long been understood in shedding light on the topological structure of sets. However, when the set is a simplicial complex and host to a dynamical process, in particular the trajectory of a canonically…
The Legendre transformation is a crucial tool in theoretical physics, known for its symmetry, especially when applied to multivariate functions. In statistical mechanics, ensembles represent the central focus. Leveraging the dimensionless…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
The present study regards the zeroth order mean field approximation of a dipole-type interaction model, which is analytically solved in the canonical and microcanonical ensembles. After writing the canonical partition function, the free and…
Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: i) Identifying $k_B\to 0$ as classical energetics, one directly derives a pair of thermodynamic variational…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…
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…