Injected power and entropy flow in a heated granular gas

– Our interest goes to the power injected in a heated granular gas and to the possibility to interpret it in terms of entropy flow. We numerically determine the distribution of the injected power by means of Monte-Carlo simulations. Then, we provide a kinetic theory approach to the computation of such a distribution function. Finally, after showing why the injected power does not satisfy a Fluctuation Relationà la Gallavotti-Cohen, we put forward a new quantity which does fulfill such a relation, and is not only applicable in a variety of frameworks outside the granular world, but also experimentally accessible. In the realm of non-equilibrium statistical physics, universal or generic results are scarce. Landmarks in the field are Einstein's seminal contribution [1] exhibiting a relation between particle current fluctuations and a response function, followed by Onsager's reciprocity [2] and the Green–Kubo relations [3, 4]. The recent discovery by Evans, Cohen and Morris [5] formalized into a mathematical theorem of general scope by Gallavotti and Cohen [6] of a symmetry property, that we will call Gallavotti–Cohen relation (GC), bearing on the entropy flux distribution therefore stands as a major progress. Similar results have been established for Markov processes by Kurchan [7] and Lebowitz and Spohn [8], with much lighter mathematics than for dynamical systems. However, mathematical as well as physical difficulties, that we shall later describe, have prevented this result to find its way towards experimental confirmation. From the point of view of probing the validity of the Gallavotti–Cohen theorem outside its mathematical domain of validity, granular gases will prove instrumental. This was indeed already realized by Aumaˆıtre et al. [9]. Yet, in the absence of a first-principle definition of entropy, a physical one, albeit heuristic, was proposed : the energy injected by the thermostat divided by the granular temperature. This is precisely the quantity simulated in [9], and considered in a recent experimental work [10]. Besides, the idea of using a macroscopic and global observable for characterizing the state of a system, instead of resorting to local c EDP Sciences