Multiplicity fluctuation from hydrodynamic noise

21 May 2014, 13:10
helium (darmstadtium)



Schlossgraben 1 64283 Darmstadt Germany
Contributed Talk New Theoretical Developments QCD phase diagram


Tetsufumi Hirano (Sophia Univ)


We discuss multiplicity fluctuation caused by noises during hydrodynamic evolution of the quark-gluon fluid created in high-energy nuclear collisions. In this talk, we claim the following non-trivial consequences within a framework of relativistic fluctuating hydrodynamics [1]: - Multiplicity (being approximately proportional to entropy) fluctuates from event to event due to hydrodynamic fluctuation of dissipative currents such as shear stress tensor and bulk pressure even if the initial state is the same in a macroscopic sense. - *Event-averaged* entropy has to increase with time so that the system obeys the second law of thermodynamics as it should be. Entropy in a certain event can, however, *decrease* with time temporarily and locally due to the hydrodynamic fluctuations. - The probability of decreasing entropy during hydrodynamic evolution is, of course, very small in general. Interestingly, the probability is quantified by the *fluctuation theorem* [2] as known in the non-equilibrium statistical mechanics. We first discuss the fluctuation theorem in non-equilibrium statistical mechanics [2]. The fluctuation theorem has been a milestone in non-equilibrium statistical mechanics since the linear response theory was established. Since the fluctuation theorem contains the Green-Kubo formula at long-time limit, it is believed to capture some important properties of non-equilibrium processes away from equilibrium. We next solve the stochastic equation for dissipative currents together with the temporal evolution equation for the energy density in one-dimensionally expanding coordinate [3] to demonstrate that the final entropy fluctuates from event to event for a given initial condition. During the time evolution of the total entropy in a certain event, reduction of the entropy occurs due to hydrodynamic fluctuation of dissipative currents. We show that the probability of decreasing entropy just obeys the above-mentioned fluctuation theorem. We finally discuss the physics consequences of hydrodynamic fluctuations on final observables. Fluctuation of the final entropy is taken over by the one of multiplicity. Thus we discuss multiplicity distribution functions from a hydrodynamic fluctuation point of view. We also discuss observables in small system such as p+p or p/d+A collisions since the effect of fluctuations are of particular importance in such smaller systems. **References** [1] K. Murase and T. Hirano, arXiv:1304.3243 [nucl-th]. [2] G. Gallavotti and E. G. Cohen, Phys. Rev. Lett. **74**, 2694 (1995); D. J. Evans and D. J. Searles, Phys. Rev. E **52**, 5839 (1995). [3] J. D. Bjorken, Phys. Rev. D **27**, 140 (1983).
On behalf of collaboration: None

Primary author

Tetsufumi Hirano (Sophia Univ)


Kenichi Nagai (Sophia University) Koichi Murase (The University of Tokyo) Ryuichi Kurita (the University of Tokyo)

Presentation Materials