Unifying fluctuation-dissipation temperatures of slow-evolving nonequilibrium systems from the perspective of inherent structures

Abstract

For nonequilibrium systems, how to define temperature is one of the key and difficult issues to solve. Although effective temperatures have been proposed and studied to this end, it still remains elusive what they actually are. Here, we focus on the fluctuation-dissipation temperatures and report that such effective temperatures of slow-evolving systems represent characteristic temperatures of their equilibrium counterparts. By calculating the fluctuation-dissipation relation of inherent structures, we obtain a temperature-like quantity TIS. For monocomponent crystal-formers, TIS agrees well with the crystallization temperature Tc, while it matches with the onset temperature Ton for glass-formers. It also agrees with effective temperatures of typical nonequilibrium systems, such as aging glasses, quasi-static shear flows, and quasi-static self-propelled flows. From the unique perspective of inherent structures, our study reveals the nature of effective temperatures and the underlying connections between nonequilibrium and equilibrium systems and confirms the equivalence between Ton and Tc.

Equilibrium States Corresponding to Targeted Hyperuniform Nonequilibrium Pair Statistics

“…Remarkably, our effective potentials yield hyperuniform deep local energy minima that are of stronger forms of hyperuniformity (measured by the class or larger α exponents) relative to the equilibrium states at unit temperature. This behavior is expected for pair potentials characterized by steep short-range repulsions, since the local minima can be regarded to be states with effectively low temperatures relative to the initial higher-temperature fluid 71 and hence the structure factor S(k) of the quench at low wavenumbers reflects stronger hyperuniformity. By contrast, the same reasoning leads to the extended proposition that a quench of an initially nonhyperuniform fluid state with such interactions to deep local energy minima have a S(0) that drops but generally not to zero, i.e., it strictly remains nonhyperuniform, as shown for three well-known models in Appendix B.…”

Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics

“…Remarkably, our effective potentials yield hyperuniform deep local energy minima that are of stronger forms of hyperuniformity (measured by the class or larger a exponents) relative to the equilibrium states at unit temperature. This behavior is expected for pair potentials characterized by steep short-range repulsions, since the local minima can be regarded to be states with effectively low temperatures relative to the initial higher-temperature fluid, 111 and hence, the structure factor S(k) of the quench at low wavenumbers reflects stronger hyperuniformity. By contrast, the same reasoning leads to the extended proposition that a quench of an initially nonhyperuniform fluid state with such interactions to deep local energy minima have an S(0) that drops but generally not to zero, i.e., it strictly remains nonhyperuniform, as shown for three wellknown models in Appendix C.…”

Fluctuations and entropy enable neural crest cell ingression

“…Stochastic transitions between different states are central to multiple biological contexts 80-83 such as cell fate changes 84-86 . Advances that equated active parameters to those of athermal systems have opened the possibility of examining thermodynamic properties of non-equilibrium, living systems 34,58,59,71-73 . By applying such an approach to test for a stochastic morphogenetic mechanism, this study complements others that have assessed thermodynamic parameters in whole organisms using calorimetry or actual temperature measurements 3,87-89 .…”

“…Proposals to explain the ingression event often invoke intriguing biochemical and physical cues 20-33 but may be incomplete since stochastic possibilities are usually not considered. Here, we apply a framework that enables thermodynamic assessment of nonequilibrium systems using effective temperature 34 in combination with empirical biophysical measurements in the mouse embryo. We find cortical fluctuations provide stochastic kicks that are essential for crossing an energy-like barrier and cell packing configurations generate an entropic trap that enables spontaneous neural crest cell ingression.…”