Related papers: Boltzmann vs Gibbs: a finite-size match
The Boltzmann-Gibbs-von Neumann entropy of a large part (of linear size L) of some (much larger) d-dimensional quantum systems follows the so-called area law (as for black holes), i.e., it is proportional to $L^{d-1}$. Here we show, for…
We construct finite-range interactions on $\mathcal{S}^{\mathbb{Z}^2}$, where $\mathcal{S}$ is a finite set, for which the associated equilibrium states (i.e., the shift-invariant Gibbs states) fail to converge as temperature goes to zero.…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…
As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: both the thermodynamic entropy of mixing and the Gibbs free energy change are zero during the formation of any ideal…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys. Rev. E 51, 3002…
We provide an extension of a recent approach to study non-equilibrium thermodynamics [Phys. Rev. E 81, 051130 (2010), to be denoted by I in this work] to inhomogeneous systems by considering the latter to be composed of quasi-independent…
A complex interplay between the academic issue about generalization of the thermodynamics and the practical matter about setting standards for a sustainable evolution of both tailored devices and natural systems is considered. It is…
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,…
We study Linear Response Theory and Entropic Fluctuations of finite dimensional non-equilibrium repeated interaction systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an…
The theory of superstatistics, originally proposed for the study of complex nonequilibrium systems, has recently been extended to studies of small systems interacting with a finite environment, because such systems display interestingly…
The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it.…
Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most…
A few decades after Hill's work on nano-thermodynamics, the development of a thermodynamic framework, to account consistently for the fluctuations of small systems due to their interactions with the surrounding environment, is still…
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we…
Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…
We discuss inertial effects in systems outside equilibrium within the framework of non-equilibrium thermodynamics. By introducing a Gibbs equation in which the entropy depends on the probability density, we are able to describe a system of…