Abstract The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have generalized the Hamilton principle to the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems, and given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, with the generalized Hamilton principle, we have given the generalized Hamiltonian for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics. PACS: 03.65.-w, 05.70.Ce, 05.30.RtAbstract The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation. In this paper, we have generalized the Hamilton principle to the generalized Hamilton principle, which can describe the open system (mass or energy exchange systems) and nonconservative force systems or dissipative systems, and given the generalized Lagrange function, it has to do with the kinetic energy, potential energy and the work of nonconservative forces to do. With the Feynman path integration, we have given the non-Hermitian quantum theory of the nonconservative force systems. Otherwise, with the generalized Hamilton principle, we have given the generalized Hamiltonian for the particle exchanging heat with the outside world, which is the sum of kinetic energy, potential energy and thermal energy, and further given the equation of quantum thermodynamics. PACS: 03.65.-w, 05.70.Ce, 05.30.Rt

arXiv:2110.04524Jun 30, 20210 citations

THE GENERAL PRINCIPLES OF QUANTUM THEORY

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

Elsevier eBooksJan 1, 19754 citations

Coordination Requires a Common Cause in Quantum Theory

Daniel Centeno, Antoine Coquet, Maria Ciudad Alañón +3 more

We propose a novel causal principle that is a genuinely multipartite extension of Reichenbach's common cause principle, namely, the coordination principle: parties in a network can achieve perfect randomized coordination--in particular, agree on a uniformly random output--only if they all share a common cause. We show that this principle does not follow from the standard no-signaling and independence principles by providing an explicit theory satisfying all these principles while violating the coordination principle. Strikingly, we prove that the coordination principle holds, however, in quantum theory for four parties, and derive noise-tolerant Bell-like inequalities that certify a common cause. We then extend these results to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause which can also be certified by experimentally accessible Bell-like inequalities. A companion paper generalizes these results for N parties, proving that the coordination principle is satisfied in general for quantum theory.We propose a novel causal principle that is a genuinely multipartite extension of Reichenbach's common cause principle, namely, the coordination principle: parties in a network can achieve perfect randomized coordination--in particular, agree on a uniformly random output--only if they all share a common cause. We show that this principle does not follow from the standard no-signaling and independence principles by providing an explicit theory satisfying all these principles while violating the coordination principle. Strikingly, we prove that the coordination principle holds, however, in quantum theory for four parties, and derive noise-tolerant Bell-like inequalities that certify a common cause. We then extend these results to a genuinely quantum coordination task, showing that the four-partite GHZ state requires a quantum common cause which can also be certified by experimentally accessible Bell-like inequalities. A companion paper generalizes these results for N parties, proving that the coordination principle is satisfied in general for quantum theory.

quant-pharXiv:2605.03120May 6, 20260 citations

Decoherence limit of quantum systems obeying generalized uncertainty principle: New paradigm for Tsallis thermostatistics

Petr Jizba B, Gaetano Lambiase, Giuseppe Gaetano Luciano +1 more

The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this paper, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis probability amplitudes, whose nonextensivity parameter $q$ monotonically increases with the GUP deformation parameter $\ensuremath{\beta}$. Second, for $\ensuremath{\beta}<0$ (i.e., $q<1$ ), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the maximal entropy principle known from estimation theory to reveal connection between the quasiclassical (decoherence) limit of GUP-related quantum theory and nonextensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasiclassical regime has relevant observational consequences. We discuss some of the implications.The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this paper, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis probability amplitudes, whose nonextensivity parameter $q$ monotonically increases with the GUP deformation parameter $\ensuremath{\beta}$. Second, for $\ensuremath{\beta}<0$ (i.e., $q<1$), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the maximal entropy principle known from estimation theory to reveal connection between the quasiclassical (decoherence) limit of GUP-related quantum theory and nonextensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasiclassical regime has relevant observational consequences. We discuss some of the implications.

arXiv:2201.07919Physical review. D/Physical review. D.Jun 15, 202245 citations

q

monotonically increases with the GUP deformation parameter $\ensuremath{\beta}$. Second, for $\ensuremath{\beta}<0$ (i.e.,

q<1

), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the maximal entropy principle known from estimation theory to reveal connection between the quasiclassical (decoherence) limit of GUP-related quantum theory and nonextensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasiclassical regime has relevant observational consequences. We discuss some of the implications.