Time-reversal symmetry, Poincaré recurrence, irreversibility, and the entropic arrow of time: From mechanics to system thermodynamics

2008 ◽  
Vol 9 (2) ◽  
pp. 250-271 ◽  
Author(s):  
Wassim M. Haddad ◽  
VijaySekhar Chellaboina ◽  
Sergey G. Nersesov
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Arrow Of Time ◽  
Poincare Recurrence ◽  
Poincaré Recurrence

scholarly journals Active gelation breaks time-reversal-symmetry of mitotic chromosome mechanics

2018 ◽  
Author(s):  
Matthäus Mittasch ◽  
Anatol W. Fritsch ◽  
Michael Nestler ◽  
Juan M. Iglesias-Artola ◽  
Kaushikaram Subramanian ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Time Reversal ◽  
Mitotic Chromosome ◽  
Metaphase Plate ◽  
Time Reversal Symmetry ◽  
Newtonian Mechanics ◽  
Arrow Of Time ◽  
Cell Nuclei ◽  
Mitotic Chromosomes ◽  
Daughter Cells

AbstractIn cell division, mitosis is the phase in which duplicated sets of chromosomes are mechanically aligned to form the metaphase plate before being segregated in two daughter cells. Irreversibility is a hallmark of this process, despite the fundamental laws of Newtonian mechanics being time symmetric.Here we show experimentally that mitotic chromosomes receive the arrow of time by time-reversal-symmetry breaking of the underlying mechanics in prometaphase. By optically inducing hydrodynamic flows within prophase nuclei, we find that duplicated chromatid pairs initially form a fluid suspension in the nucleoplasm: although showing little motion on their own, condensed chromosomes are free to move through the nucleus in a time-reversible manner. Actively probing chromosome mobility further in time, we find that this viscous suspension of chromatin transitions into a gel after nuclear breakdown. This gel state, in which chromosomes cannot be moved by flows, persists even when chromosomes start moving to form the metaphase plate. Complemented by minimal reconstitution experiments, our active intra-nuclear micro-rheology reveals time-reversal-symmetry breaking of chromosome mechanics to be caused by the transition from a purely fluid suspension into an active gel.Graphical abstractOne sentence summaryFlows induced in living cell nuclei reveal the rheological changes that bring chromosomes under mechanical control during mitosis.

scholarly journals Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 380 ◽  
Author(s):  
Naomichi Hatano ◽  
Gonzalo Ordonez
Keyword(s):  
Time Reversal ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Functional Space ◽  
Time Reversal Symmetry ◽  
Arrow Of Time ◽  
Initial State ◽  
Resonant States ◽  
Complex Eigenvalues

It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called “unphysical”, they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for t > 0 ; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamic ending at a time-reversal symmetric final state is dominated by the anti-resonant states for t < 0 .

scholarly journals Odd Willis coupling induced by broken time-reversal symmetry

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Li Quan ◽  
Simon Yves ◽  
Yugui Peng ◽  
Hussein Esfahlani ◽  
Andrea Alù
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Acoustic Metamaterials ◽  
Asymmetric Structures ◽  
Sound Control ◽  
Wavefront Shaping ◽  
Scattering Response ◽  
Symmetric Structures ◽  
Signal Routing ◽  
Broad Interest

AbstractWhen sound interacts with geometrically asymmetric structures, it experiences coupling between pressure and particle velocity, known as Willis coupling. While in most instances this phenomenon is perturbative in nature, tailored asymmetries combined with resonances can largely enhance it, enabling exotic acoustic phenomena. In these systems, Willis coupling obeys reciprocity, imposing an even symmetry of the Willis coefficients with respect to time reversal and the impinging wave vector, which translates into stringent constraints on the overall scattering response. In this work, we introduce and experimentally observe a dual form of acoustic Willis coupling, arising in geometrically symmetric structures when time-reversal symmetry is broken, for which the pressure-velocity coupling is purely odd-symmetric. We derive the conditions to maximize this effect, we experimentally verify it in a symmetric subwavelength scatterer biased by angular momentum, and we demonstrate the opportunities for sound scattering enabled by odd Willis coupling. Our study opens directions for acoustic metamaterials, with direct implications for sound control, non-reciprocal scattering, wavefront shaping and signal routing, of broad interest also for nano-optics, photonics, elasto-dynamics, and mechanics.

scholarly journals Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Harald Pleiner ◽  
Helmut R. Brand
Keyword(s):  
Electric Fields ◽  
Time Reversal ◽  
Liquid Crystalline ◽  
Second Law Of Thermodynamics ◽  
Time Reversal Symmetry ◽  
Local Conservation ◽  
Continuous Symmetry ◽  
Polar Order ◽  
Preferred Direction ◽  
Symmetry Properties

Abstract We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.

scholarly journals Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vadim Grinenko ◽  
Debarchan Das ◽  
Ritu Gupta ◽  
Bastian Zinkl ◽  
Naoki Kikugawa ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Symmetry Breaking ◽  
Time Reversal ◽  
Order Parameter ◽  
Muon Spin Rotation ◽  
Horizontal Line ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Symmetry Protected ◽  
Line Node

AbstractThere is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz order.

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