Related papers: Alternative Derivation of the Partition Function f…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
In this chapter, we present a straightforward geometrical argument that in a certain way recalls us the equivalence between the canonical and the microcanonical ensembles in the thermodynamic limit for the particular context of physical…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
For a closed bi-partite quantum system partitioned into system proper and environment we interprete the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible…
This work extends a recently developed mathematical theory of thermodynamics for Markov processes with, and more importantly, without detailed balance. We show that the Legendre transform in connection to ensemble changes in Gibbs'…
We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two novel statistical quantities: a learning capacity and…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the…
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 present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
When we consider canonical average for classical discrete systems under constant composition (specifically, substitutional alloys) as a map phi from a set of many-body interatomic interactions to that of microscopic configuration in…
The analytic continuation from the Euclidean domain to real space of the one-particle irreducible quantum effective action is discussed in the context of generalized local equilibrium states. Discontinuous terms associated with dissipative…
In standard thermodynamics, internal energy is a state function, independent of process rates. We show that this structure breaks down in open quantum systems undergoing thermalization. Within Gorini-Kossakowski-Lindblad-Sudarshan (GKLS)…
We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen…