Perturbative expansion of irreversible works in symmetric and asymmetric processes

• URL: http://arxiv.org/abs/2201.03693v2
• Date: Tue, 8 Feb 2022 01:10:47 GMT
• Title: Perturbative expansion of irreversible works in symmetric and asymmetric processes
• Authors: T. Koide
• Abstract summary: We obtain a new formula to calculate the mean work perturbatively which is applicable to systems with degeneracy in the eigenvalues of the Fokker-Planck operator. This method enables us to study how the geometrical symmetry affects thermodynamic description of a Brownian particle.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work perturbatively which is applicable to systems with degeneracy in the eigenvalues of the Fokker-Planck operator. This method enables us to study how the geometrical symmetry affects thermodynamic description of a Brownian particle. To illustrate the application of the derived theory, we consider the Fokker-Planck equation with a two-dimensional harmonic potential. To investigate the effect of symmetry of the potential, we study thermodynamic properties in symmetric and asymmetric deformation processes of the potential: the rotational symmetry of the harmonic potential is held in the former, but it is broken in the latter. Optimized deformations in these processes are defined by minimizing mean works. Comparing these optimized processes, we find that the difference between the symmetric and asymmetric processes is maximized when the deformation time of the potential is given by a critical time which is characterized by the relaxation time of the Fokker-Planck equation. This critical time in the mean work is smaller than that of the change of the mean energy because of the hysteresis effect in the irreversible processes.

Related papers

• Asymmetry Amplification by a Nonadiabatic Passage through a Critical Point [0.0]
  We propose and solve a minimal model of dynamic passage through a quantum second order phase transition in the presence of weak symmetry breaking interactions and no dissipation. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry breaking term is. This suggests a potential mechanism for strong asymmetry in the production of particles with almost identical characteristics.
  arXiv  Detail & Related papers  (2024-08-28T16:06:56Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
  entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented. We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
  arXiv  Detail & Related papers  (2024-04-04T14:45:28Z)
• Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems [0.0]
  The quantum Mpemba effect is the counter-intuitive non-equilibrium phenomenon wherein the dynamic restoration of a broken symmetry occurs more rapidly when the initial state exhibits a higher degree of symmetry breaking. Here we focus on a two-dimensional free-fermion lattice employing the entanglement asymmetry as a measure of symmetry breaking. We find that the quantum Mpemba effect is strongly affected by the size of the system in the transverse dimension, with the potential to either enhance or spoil the phenomenon depending on the initial states.
  arXiv  Detail & Related papers  (2024-03-07T13:38:40Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup [0.3957768262206625]
  We extend Noether's theorem to a class of significant PT -symmetric systems. We experimentally investigate the extended Noether's theorem in PT -symmetric single-qubit and two-qubit systems.
  arXiv  Detail & Related papers  (2023-01-18T05:32:06Z)
• Simulating scalar field theories on quantum computers with limited resources [62.997667081978825]
  We present a quantum algorithm for implementing $phi4$ lattice scalar field theory on qubit computers. The algorithm allows efficient $phi4$ state preparation for a large range of input parameters in both the normal and broken symmetry phases.
  arXiv  Detail & Related papers  (2022-10-14T17:28:15Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Noether's Learning Dynamics: The Role of Kinetic Symmetry Breaking in Deep Learning [7.310043452300738]
  In nature, symmetry governs regularities, while symmetry breaking brings texture. Recent experiments suggest that the symmetry of the loss function is closely related to the learning performance. We pose symmetry breaking as a new design principle by considering the symmetry of the learning rule in addition to the loss function.
  arXiv  Detail & Related papers  (2021-05-06T14:36:10Z)
• Symmetry Breaking in Symmetric Tensor Decomposition [44.181747424363245]
  We consider the nonsymmetry problem associated with computing the points rank decomposition of symmetric tensors. We show that critical points the loss function is detected by standard methods.
  arXiv  Detail & Related papers  (2021-03-10T18:11:22Z)
• Relativistic electron-impact ionization of hydrogen atom from its metastable 2S-state in the symmetric/asymmetric coplanar geometries [0.0]
  We analytically compute, in the first Born approximation for symmetric and asymmetric coplanar geometries. The process is investigated by using the relativistic Dirac-formalism.
  arXiv  Detail & Related papers  (2020-08-20T11:58:14Z)

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.