Related papers: On Entropy Minimization and Convergence
We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…
We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a…
We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with…
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…
We analyze a gas of noninteracting fermions confined to a one-dimensional harmonic oscillator potential, with the aim of distinguishing between two proposed definitions of the thermodynamic entropy in the microcanonical ensemble, namely the…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability…
The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy…
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…
When studying the thermodynamic properties of mesoscopic systems the most appropriate microcanonical entropy is the volume entropy, i.e. the logarithm of the volume of phase space enclosed by the hypersurface of constant energy. For systems…
We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
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…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
The issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…