arXiv subjects

Thomas Oikonomou

Publications and source records attributed to Thomas Oikonomou.

At least 19 recordsLinked to original sources

arXiv2026

Catalytic quantum thermodynamics beyond additivity and reduced-state monotones

The generalized second laws of quantum thermodynamics are usually formulated in terms of Rényi divergences and the associated family of generalized free energies. In catalytic thermal transformations, this framework typically certifies the existence of a suitable catalyst but does not make the catalytic contribution explicit in the resulting system-level inequalities. Here we develop a complementary formulation based on non-additive divergences, whose pseudo-additive structure yields a family of generalized free energies with an explicit catalyst-dependent correction term. For uncorrelated catalytic thermal transformations, we show that this leads to non-additive second-law relations that make the catalytic contribution explicit and provide nontrivial constraints on admissible catalysts when the catalyst is returned only approximately. We also analyze correlated catalytic thermal transformations and show, through explicit finite-dimensional examples, that reduced-state data are generally insufficient to characterize thermodynamic accessibility: the thermo-majorization behavior of the joint transformation can change while the system and catalyst marginals remain fixed, and even states with identical marginals and the same mutual information can exhibit different thermo-majorization accessibility. Our results show that non-additivity can be thermodynamically informative in uncorrelated catalysis, whereas correlated catalysis generally requires a genuinely joint-state-sensitive description beyond reduced-state monotones.

quant-ph↗

arXiv2026

Particle Mechanics from Local Energy Conservation

We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a variational principle. Starting from the instantaneous condition $\dot{E}=0$, imposed as a pointwise constraint along a particle trajectory, we obtain a generalized force law that does not assume a specific kinetic-energy function, momentum-velocity relation, or equation of motion. The resulting inertial response naturally decomposes into a component parallel to the acceleration, responsible for changes in kinetic energy, and a transverse component that preserves energy while altering the direction of motion. Imposing rotational equivariance constrains the geometric structure of the force law, while the relativity principle between inertial reference frames further restricts its admissible realizations. In strictly one-dimensional motion, inertial-frame equivalence implies invariance of the total force under inertial boosts; together with local energy conservation, this uniquely fixes the functional form of kinetic energy and momentum. Galilean invariance selects the Newtonian expressions, whereas Lorentz invariance yields the relativistic ones. The framework unifies conservative and non-conservative (yet non-dissipative) dynamics at the single-particle level and clarifies the precise conditions under which energy-based and variational formulations of mechanics are dynamically equivalent. Newtonian and relativistic mechanics thus emerge as symmetry-selected realizations of a common energy-conserving force-energy structure.

physics.class-ph↗

arXiv2023

Multipartite Correlated Majorization Criteria for Finite Discrete Probability

In this paper we study multipartite and correlated majorization of the finite discrete probability distributions emerging in quantum information theory. We start proving the subadditivity of the Rényi and Burg entropies, and we show that the criteria for such a generalized majorization scheme can be provided solely in terms of the Rényi and Burg entropies. Surprisingly, the same set of criteria applies both to the correlated and uncorrelated cases. Finally, based on our findings in majorization, we give a proof of the characterization of the Rényi and Burg entropies in terms of continuity, symmetry and (sub)additivity.

cond-mat.stat-mech↗

arXiv2020

Stability Properties of 1-Dimensional Hamiltonian Lattices with Non-analytic Potentials

We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from non-analytic potentials. In particular, we study the dynamics of a model governed by a "graphene-type" force law and one inspired by Hollomon's law describing "work-hardening" effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of non-analytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles $N$ and the total energy $E$ are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for large $N$, it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.

nlin.CD↗

arXiv2019

Reply to "Comment on `Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data' "

We reply to the Comment by Jizba and Korbel [arXiv:1905.00729v1] by first pointing out that the Schur-concavity proposed by them falls short of identifying the correct intervals of normalization for the optimum probability distribution even though normalization is a must ingredient in the entropy maximization procedure. Secondly, their treatment of the subset independence axiom requires a modification of the Lagrange multipliers one begins with thereby rendering the optimization less trustworthy. We also explicitly demonstrate that the Rényi entropy violates the subset independence axiom and compare it with the Shannon entropy. Thirdly, the new composition rule offered by Jizba and Korbel are shown to yield probability distributions even without a need for the entropy maximization procedure at the expense of creating artificial bias in the data.

cond-mat.stat-mech↗

arXiv2019

Stationary Worldline Power Distributions

A worldline with a time-independent spectrum is called stationary. Such worldlines are arguably the most simple motions in physics. Barring the trivially static motion, the non-trivial worldlines are uniformly accelerated. As such, a point charge moving along a stationary worldline will emit constant radiative power. The angular distribution, maximum angle scaling and Thomas precession of this power is found for all stationary worldlines including those with torsion and hypertorsion.

gr-qc↗

arXiv2019

Opening Pandora's Box: Maximizing the $q$-entropy with Escort Averages

It is currently a widely used practice to write the constraints in terms of escort averages when the generalized entropies are employed in the maximization scheme. We show that the maximization of the nonadditive $q$-entropy with escort averages leads either to an overall lack of connection with thermodynamics or violation of the second and third laws of thermodynamics if one adopts the Clausius definition of the physical temperature. If an alternative definition of physical temperature is chosen by respecting the divisibility of the total system into independent subsystems, thermodynamic relations are restored albeit at the cost of transforming the nonadditive $q$-entropy into the Rényi entropy. These results are illustrated by studying the quantum mechanical free particle.

cond-mat.stat-mech↗

arXiv2019

Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data

We show that the Rényi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite-size of the data despite being additive. It is demonstrated that this is so because it does not conform to the system and subset independence axioms of Shore and Johnson. We finally show that the escort averaged constraints do not remedy the situation.

cond-mat.stat-mech↗

arXiv2018

Overcoming the Artificial Biases for the Nonadditive $ q $-Entropy

Entropy maximization procedure has been a general practice in many diverse fields of science to obtain the concomitant probability distributions. The consistent use of the maximization procedure on the other hand requires the probability distributions to obey the probability multiplication rule for independent events. However, despite that the nonadditive $ q $-entropy is known not to obey this rule, it is still used with the entropy maximization procedure to infer the probability distributions at the expense of creating artificial biases not present in the data itself. Here we show that this important obstacle can be overcome by considering the intrinsic discrete structure and related averaging scheme of the nonadditive $ q $-entropy. This also paves the road to a better understanding of the entropy maximization procedure of Jaynes.

cond-mat.stat-mech↗

arXiv2018

Symbolic Dynamics of Music from Europe and Japan

After a brief introduction to the theory underlying block-entropy, and its relation to the dynamics of complex systems as well as certain information theory aspects, we study musical texts coming from two distinct musical traditions (Japanese and Western European) encoded via symbolic dynamics. We quantify their information content or also known as the degree of "non-randomness" which essentially defines the complexity of the text. We analyse the departure of "total randomness" to the constrains underlying the dynamics of the symbol generating process. Following Shannon on his attribution to these constraints as the emergence of complexity, we observe that it can be accurately assessed by the texts' block-entropy versus block-length scaling laws.

nlin.CD↗

arXiv2018

Discrete and Weyl density of states for photons and phonons

The current density of states (DOS) calculations do not take into account the essential discreteness of the state space, since they rely on the unbounded continuum approximation. Recently, discrete DOS based on the quantum-mechanically allowable minimum energy interval has been introduced for quadratic dispersion relation. In this work, we consider systems exhibiting linear dispersion relation, particularly photons and phonons, and calculate the related density and number of states (NOS). Also, a Weyl's conjecture-based DOS function is calculated for photons and phonons by considering the bounded continuum approach. We show that discrete DOS function reduces to expressions of bounded and unbounded continua in the appropriate limits. The fluctuations in discrete DOS completely disappear under accumulation operators. It's interesting that relative errors of NOS and DOS functions with respect to discrete ones are exactly the same as the ones for quadratic dispersion relation. Furthermore, the application of discrete and Weyl DOS for the calculation of internal energy of a photon gas is presented and importance of discrete DOS is discussed. It's shown that discrete DOS function given in this work needs to be used whenever the low energy levels of a physical system are heavily occupied.

cond-mat.stat-mech↗

arXiv2018

Reply to the comment on "Route from discreteness to the continuum for the Tsallis $q$-entropy" by Congjie Ou and Sumiyoshi Abe

It has been known for some time that the usual $q$-entropy $S_q^{(n)}$ cannot be shown to converge to the continuous case. In [Phys. Rev. E 97 (2018) 012104], we have shown that the discrete $q$-entropy $\widetilde{S}_q^{(n)}$ converges to the continuous case when the total number of states are properly taken into account in terms of a convergence factor. Ou and Abe [Phys. Rev. E 97, (2018) 066101, arXiv:1801.03035] noted that this form of the discrete $q$-entropy does not conform to the Shannon-Khinchin expandability axiom. As a reply, we note that the fulfillment or not of the expandability property by the discrete $q$-entropy strongly depends on the origin of the convergence factor, presenting an example in which $\widetilde{S}_q^{(n)}$ is expandable.

cond-mat.stat-mech↗

arXiv2018

Entropy Maximization with Linear Constraints: The Uniqueness of the Shannon Entropy

Within a framework of utmost generality, we show that the entropy maximization procedure with linear constraints uniquely leads to the Shannon-Boltzmann-Gibbs entropy. Therefore, the use of this procedure with linear constraints should not be extended to the generalized entropies introduced recently. In passing, it is remarked how the forceful use of the entropy maximization for the Tsallis and Rényi entropies implies either the Shannon limit of these entropies or self-referential contradictions. Finally, we note that the utilization of the entropy maximization procedure with different averaging schemes is beyond the scope of this work.

cond-mat.stat-mech↗

arXiv2018

Reply to "Rescuing the MaxEnt treatment for $q$-generalized entropies" by A. Plastino and M.C. Rocca

Plastino and Rocca [Physica A 491, 1023 (2018)] recently criticized our work [Phys. Lett. A 381, 207 (2017)] on the ground that one should use functional calculus instead of the ordinary calculus adopted by us in the entropy maximization procedure. We simply point out that our work requires right from the beginning $\partial S_q / \partial U = β$, whereas the formalism of Plastino and Rocca yields $\partial S_q/\partial U = q βZ^{1-q} \neq β$. Therefore, the work of Plastino and Rocca is irrelevant for our work.

cond-mat.stat-mech↗

arXiv2018

Impossible Mission: Entropy Maximization with Escort Averages

It has recently been a common practice to maximize the deformed entropies through the escort averaging scheme. However, whatever averaging procedure is employed, one should recover the ordinary Shannon maximization results in the appropriate limit of the deformation parameter e.g. $q\to 1$ for the Tsallis and Rényi entropies. Otherwise, the very meaning of a consistent generalization becomes at stake. Using only this equivalence, we show that any deformed entropy expression, maximized with the escort averaged constraints, yields that the Shannon entropy $S$ is equal to the logarithm of the ordinary canonical partition function i.e. $S = \ln(Z_S )$ instead of the correct thermodynamic relation $S = βU + \ln(Z_S )$. Therefore, we conclude that the use of the escort averaging procedure should be avoided for any deformed entropies, since it cannot even yield the well-known thermodynamic relations of the ordinary canonical formalism.

cond-mat.stat-mech↗

arXiv2018

Route from discreteness to the continuum for the non-logarithmic $q$-entropy

The existence and exact form of the continuum expression of the discrete nonlogarithmic $q$-entropy is an important open problem in generalized thermostatistics, since its possible lack implies that nonlogarithmic $q$-entropy is irrelevant for the continuous classical systems. In this work, we show how the discrete nonlogarithmic $q$-entropy in fact converges in the continuous limit and the negative of the $q$-entropy with continuous variables is demonstrated to lead to the (Csisz{á}r type) $q$-relative entropy just as the relation between the continuous Boltzmann-Gibbs expression and the Kullback-Leibler relative entropy. As a result, we conclude that there is no obstacle for the applicability of the $q$-entropy to the continuous classical physical systems.

cond-mat.stat-mech↗

arXiv2017

Comment on "Troublesome aspects of the Renyi-MaxEnt treatment" by A. Plastino, M.C. Rocca and F. Pennini

Plastino, Rocca and Pennini [Phys. Rev. E \textbf{94} (2016) 012145] recently stated that the Rényi entropy is not suitable for thermodynamics by using functional calculus, since it leads to anomalous results unlike the Tsallis entropy. We first show that the Tsallis entropy also leads to such anomalous behaviours if one adopts the same functional calculus approach. Second, we note that one of the Lagrange multipliers is set in an \textit{ad-hoc} manner in the functional calculus approach of Plastino, Rocca and Pennini. Finally, the explanation for these anomalous behaviours is provided by observing that the generalized distributions obtained by Plastino, Rocca and Pennini does not yield the ordinary canonical partition function in the appropriate limit and therefore cannot be considered as genuine generalized distributions.

cond-mat.stat-mech↗

arXiv2017

On a Uniformly Accelerated Point Charge moving along a Cusp

A uniformly accelerated point charge which moves neither in a straight line nor in a circle, but in a cusp, is investigated. We find the angular distribution of the Larmor radiation, the constant power, and the intensity in the maximal direction. It is found that the intensity of uniformly accelerated cusp motion scales like non-uniformly accelerated synchrotron radiation. We confirm the exact vacuum excitation spectra of quantized field detectors on the world line.

physics.class-ph↗