Related papers: Features of constrained entropic functional variat…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $\rho$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space…
Several implications of well-known fluctuation theorems, on the statistical properties of the entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a…
Finite heat reservoir capacity and temperature fluctuations lead to modification of the well known canonical exponential weight factor. Requiring that the corrections least depend on the one-particle energy, we derive a deformed entropy,…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs…
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
In a recent companion paper, we observed that the rules of ordinary thermodynamics generally fail to respect thermal duality, a symmetry of string theory under which the physics at temperature T is related to the physics at the inverse…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
The thermal partition function, $Z$, of a $CFT_d$ on $S^{d-1}$ is parameterized by the inverse temperature $\beta$ along with $\lfloor d/2\rfloor$ angular velocities $\omega_i$. In this paper, we investigate the behaviour of this partition…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
It was recently shown, starting from first principles, that thermodynamics' first law (TFL) can be microscopically obtained without need of invoking the adiabatic theorem (AT) [Physica A, {\bf 356}, 167 (2005)]. We show here that a TFL can…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
It is often incorrectly assumed that the number of microstates \Omega (E,V,N,...) available to an isolated system can have arbitrary dependence on the extensive variables E,V,N, .... However, this is not the case for natural systems which…