Symmetry for the duration of entropy-consuming intervals

Abstract

We introduce the violation fraction υ as the cumulative fraction of time that a mesoscopic system spends consuming entropy at a single trajectory in phase space. We show that the fluctuations of this quantity are described in terms of a symmetry relation reminiscent of fluctuation theorems, which involve a function, Φ, which can be interpreted as an entropy associated to the fluctuations of the violation fraction. The function Φ, when evaluated for arbitrary stochastic realizations of the violation fraction, is odd upon the symmetry transformations which are relevant for the associated stochastic entropy production. This fact leads to a detailed fluctuation theorem for the probability density function of Φ. We study the steady-state limit of this symmetry in the paradigmatic case of a colloidal particle dragged by optical tweezers through an aqueous solution. Finally, we briefly discuss on possible applications of our results for the estimation of free-energy differences from single molecule experiments.

Interplay between shape-phase transitions and shape coexistence in the Zr isotopes

“…bosons, which are subsequently mixed. The resulting interacting boson model with configuration mixing (IBM-CM) [33,34] has been used extensively for describing configuration-mixed QPTs and coexistence phenomena in nuclei [33][34][35][36][37][38][39][40][41][42][43][44]. In this case, the quantum Hamiltonian has a matrix form [39]…”

“…The calculated observables are then compared with the measured values. The adapted fitting procedure is similar to that used in [35][36][37][38][39][40][41][42]. We allow a gradual change of the parameters between adjacent isotopes, but take into account the proposed shell-model interpretation for the structure evolution in this region [2][3][4].…”

Partial dynamical symmetries and shape coexistence in nuclei

“…The above discussion has focused on the dynamics in the vicinity of the critical point where the spherical and deformed minima are near degenerate. The evolution of structure away from the critical point can be studied by incorporating additional terms intoĤ (22). Adding an n d term, will leave the solvable spherical states (21) unchanged, but will shift the deformed ground band to higher energy of order 2 N/3.…”

“…In a shell model description of nuclei near shell-closure, it is attributed to the occurrence of multi-particle multi-hole intruder excitations across shell gaps. For medium-heavy nuclei, this necessitates drastic truncations of large model spaces, e.g., by Monte Carlo sampling [14,15] or by a bosonic approximation of nucleon pairs [16][17][18][19][20][21][22][23][24][25]. In a mean-field approach, based on energy density functionals, the coexisting shapes are associated with different minima of an energy surface calculated self-consistently.…”

Intertwined quantum phase transitions in the Zr chain

“…We call for sake of clarity these phase transitions Type II [3], to distinguish them from those of a single configuration. Type II QPTs have been observed in nuclei near shell closure, e.g., in the light Pb-Hg isotopes [4], albeit with strong mixing between the two configurations. In the present contribution, we explore a situation where in parallel to the crossing, each configuration maintains its purity and its own shape-evolution with nucleon number.…”