Related papers: Microcanonical entropy for classical systems
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
It is shown that the recently introduced singularities of the microcanonical entropy like "microcanonical phase transitions", and exotic pattern of the microcanonical caloric curve T(E) like multi-valuednes or the appearance of "dinosaur's…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
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…
We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. This theory allows to reformulate Bachmann's classification of PTs for finite-size systems in terms of geometric properties of…
We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the…
Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
The quest for a microscopic foundation of Thermodynamics is addressed within the Nonunitary Newtonian Gravity model through the study of a specific closed system, namely a three-dimensional harmonic nanocrystal. A numerical calculation of…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
We develop new modified cosmological scenarios by applying the first law of thermodynamics at the Universe horizon, utilizing a new entropic functional that generalizes the standard Boltzmann-Gibbs-Shannon entropy. In particular, starting…
We show that the canonical finite size scaling of the specific heat emerges naturally - and in some sense trivially - from the assumption that the microcanonical specific entropy exhibits no substantial system size dependence.
The microscopic derivation of the second law for macroscopic system is given under the phenomenological assumption that both the initial and final states are described by mutually different canonical ensembles. In particular, it is also…
We show that entropy is globally concave with respect to energy for a rich class of mean field interactions, including regularizations of the the point-vortex model in the plane, plasmas and self-gravitating matter in 2D, as well as the…
A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum…
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…