arXiv subjects

G. Baris Bagci

Publications and source records attributed to G. Baris Bagci.

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↗

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↗

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

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

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↗

arXiv2016

Misusing the entropy maximization in the jungle of generalized entropies

It is well-known that the partition function can consistently be factorized from the canonical equilibrium distribution obtained through the maximization of the Shannon entropy. We show that such a normalized and factorized equilibrium distribution is warranted if and only if the entropy measure $I \{(p_i)\}$ has an additive slope i.e. $\partial I \{(p_i)\} / \partial p_i$ when the ordinary linear averaging scheme is used. Therefore, we conclude that the maximum entropy principle of Jaynes should not be used for the justification of the partition functions and the concomitant thermodynamic observables for generalized entropies with non-additive slope. Finally, Tsallis and Rényi entropies are shown not to yield such factorized canonical-like distributions.

cond-mat.stat-mech↗

arXiv2016

The Canonical Distribution without Thermodynamic Limit

We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not use the usual equal a priori probability postulate. We numerically demonstrate the implications of our derivation for the free and oscillating molecules.

cond-mat.stat-mech↗

arXiv2016

Group theory, entropy and the third law of thermodynamics

Curado \textit{et al.} [Ann. Phys. \textbf{366} (2016) 22] have recently studied the axiomatic structure and the universality of a three-parameter trace-form entropy inspired by the group-theoretical structure. In this work, we study the group-theoretical entropy $S_{a,b,r}$ in the context of the third law of thermodynamics where the parameters $\left\lbrace a,b,r \right\rbrace $ are all independent. We show that this three-parameter entropy expression can simultaneously satisfy the third law of thermodynamics and the three Khinchin axioms, namely continuity, concavity and expansibility only when the parameter $b$ is set to zero. In other words, it is thermodynamically valid only as a two-parameter generalization $S_{a,r}$. Moreover, the restriction set by the third law i.e., the condition $b = 0$, is important in the sense that the so obtained two-parameter group-theoretical entropy becomes extensive only when this condition is met. We also illustrate the interval of validity of the third law using the one-dimensional Ising model with no external field. Finally, we show that the $S_{a,r}$ is in the same universality class as that of the Kaniadakis entropy for $0 < r < 1$ while it has a distinct universality class in the interval $-1 < r < 0$.

cond-mat.stat-mech↗

arXiv2016

Validity of the third law of thermodynamics for the Tsallis entropy

Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] recently stated that the Tsallis entropy violates the third law of thermodynamics for $0 < q <1$ in the sub-additive regime. We first show that the division between the regimes $q < 1$ and $q > 1$ is already inherent in the fundamental incomplete structure of the deformed logarithms and exponentials underlying the Tsallis entropy. Then, we provide the complete deformed functions and show that the Tsallis entropy conforms to the third law of thermodynamics for both super-additive $q < 1$ and sub-additive $q > 1$ regimes. Finally, we remark that the Tsallis entropy does not require the use of escort-averaging scheme once it is expressed in terms of the complete deformed functions.

cond-mat.stat-mech↗

arXiv2015

Comment on "Third Law of thermodynamics as a key test of generalized entropies"

Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] state that the Tsallis entropy violates the third law of thermodynamics for $q \leq 0$ and $0<q<1$. We show that their results are valid only for $q \geq 1$, since there is no distribution maximizing the Tsallis entropy for the intervals $q \leq 0$ and $0<q<1$ compatible with the system energy expression.

cond-mat.stat-mech↗