Related papers: Tropical Limit in Statistical Physics
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
The physical quantity "temperature" is a cornerstone of thermodynamics and statistical physics. But it is necessary to mention that very frequently the scientists forget about the conditions to be satisfied in order to introduce…
The applicability conditions of a recently reported Central Limit Theorem-based approximation method in statistical physics are investigated and rigorously determined. The failure of this method at low and intermediate temperature is proved…
Statistical mechanics reveals that the properties of a macroscopic physical system emerge as an average over an ensemble of statistically independent microscopic subsystems, each occupying a specific microstate. In the study of quantum…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
We revisit the Rayleigh--Riabouchinsky paradox in dimensional analysis by making explicit the bridge between thermodynamics and the mechanical interpretation of temperature. Boltzmann's constant $k_B$ acts as a dimensional unifier, leading…
The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…
The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…
A thermodynamic system of non-interacting quantum particles changes its statistical distribution formulas if there is a universal limitation for the size of energetic quantum leaps (magnitude of quantum leaps smaller than Planck energy). By…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…