Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics

• URL: http://arxiv.org/abs/2308.12368v1
• Date: Wed, 23 Aug 2023 18:16:15 GMT
• Title: Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Authors: Petr Jizba, Gaetano Lambiase, Giuseppe Gaetano Luciano and Luciano Petruzziello
• Abstract summary: We study coherent states associated to a generalized uncertainty principle (GUP) We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study GUP in terms of non-extensive thermodynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study coherent states associated to a generalized uncertainty principle (GUP). We separately analyze the cases of positive and negative deformation parameter $\beta$, showing that the ensuing probability distribution is a Tsallis distribution whose non-extensivity parameter $q$ is monotonically related to $\beta$. Moreover, for $\beta <0$ (corresponding to $q<1$), we reformulate the GUP in terms of a one-parameter class of Tsallis entropy-power based uncertainty relations, which are again saturated by the GUP coherent states. We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study quasi-classical regime of GUP in terms of non-extensive thermodynamics. We substantiate our claim by discussing generalization of Verlinde's entropic force and ensuing implications in the late-inflation epoch. Corresponding dependence of the $\beta$ parameter on cosmological time is derived for the reheating epoch. The obtained $\beta$ is consistent with values predicted by both string-theory models and the naturalness principle. Further salient issues, including derivation of new $\beta$-dependent expressions for the lowest possible value of the spin and Immirzi parameter in Loop Quantum Gravity, and connection of our proposal with the Magueijo--Smolin doubly special relativity are also discussed. This article provides a more extended and comprehensive treatment of our recent letter [Phys. Rev. D 105, L121501 (2022)].

Related papers

• A family of thermodynamic uncertainty relations valid for general fluctuation theorems [0.0]
  We derive a family of TURs that explores higher order moments of the entropy production. The resulting bound holds in both classical and quantum regimes. We draw a connection between our TURs and the existence of correlations between the entropy production and the thermodynamic quantity under consideration.
  arXiv  Detail & Related papers  (2024-07-15T02:00:53Z)
• Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences [49.853843995972085]
  The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is presented. Examples of the solution for particular choices of the function $f$ are presented.
  arXiv  Detail & Related papers  (2024-02-01T11:12:00Z)
• New insights on the quantum-classical division in light of Collapse Models [63.942632088208505]
  We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
  arXiv  Detail & Related papers  (2022-10-19T14:51:21Z)
• Stability and Risk Bounds of Iterative Hard Thresholding [41.082982732100696]
  We introduce a novel sparse generalization theory for IHT under the notion of algorithmic stability. We show that IHT with sparsity level $k$ enjoys an $mathcaltilde O(n-1/2sqrtlog(n)log(p))$ rate of convergence in sparse excess risk. Preliminary numerical evidence is provided to confirm our theoretical predictions.
  arXiv  Detail & Related papers  (2022-03-17T16:12:56Z)
• Robust PAC$^m$: Training Ensemble Models Under Misspecification and Outliers [46.38465729190199]
  PAC-Bayes theory demonstrates that the free energy criterion minimized by Bayesian learning is a bound on the generalization error for Gibbs predictors. This work presents a novel robust free energy criterion that combines the generalized score function with PAC$m$ ensemble bounds.
  arXiv  Detail & Related papers  (2022-03-03T17:11:07Z)
• Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics [0.0]
  We study possible observational effects of generalized uncertainty principle (GUP) systems in their decoherence domain. We invoke the Maximal Entropy principle known from estimation theory to reveal connection between the quasi-classical (decoherence) limit of GUP-related quantum theory and non-extensive thermostatistics of Tsallis.
  arXiv  Detail & Related papers  (2022-01-19T23:37:05Z)
• R\'enyi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations [91.3755431537592]
  We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence. We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
  arXiv  Detail & Related papers  (2021-06-19T04:06:23Z)
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme [8.37609145576126]
  The relative entropy of entanglement $E_Rite is defined as the distance of a multi-part quantum entanglement from the set of separable states as measured by the quantum relative entropy. We show that this state is always achieved, i.e. any state admits a closest separable state, even in dimensions; also, $E_Rite is everywhere lower semi-negative $lambda_$quasi-probability distribution.
  arXiv  Detail & Related papers  (2021-05-17T18:03:02Z)
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes [2.5454615592832917]
  We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state $rho$. We show that this additional EP, which we term the "mismatch cost of $rho$", has a universal information-theoretic form.
  arXiv  Detail & Related papers  (2021-03-09T22:03:02Z)
• The variance of relative surprisal as single-shot quantifier [0.0]
  We show that (relative) surprisal gives sufficient conditions for approximate state-transitions between pairs of quantum states in single-shot setting. We further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy.
  arXiv  Detail & Related papers  (2020-09-17T16:06:54Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.