## Title

**Non-equilibrium identities and nonlinear response theory for granular fluids**

## Abstract

Although it has been believed that non-equilibrium identities such as the fluctuation theorem
are supported by the local time-reversal symmetry or the detailed balance condition,
some experiments and theoretical papers[1-3] suggest
the existence of fluctuation theorem or related equation even in granular systems
which do not have neither any time reversal symmetry nor the detailed balance.

To clarify the reason why we observe such identities, we develop the general formalism
which can be applied to any dissipative classical systems,
and derive some non-equilibrium identities such as the integral fluctuation theorem (IFT),
Jarzynski equality and the generalized Green-Kubo formula starting from an arbitrary non-equilibrium state.[4]

In particular, the existence of IFT directly leads to the corresponding law to the second law of thermodynamics.
The validity of these identities have been verified through the numerical simulation for sheared granular fluids.[4]

1. K. Feitosa and N. Mennon, Phys. Rev. Lett. 92, 164301 (2004):
N. Kumar, S. Ramaswamy and A. K. Sood, Phys. Rev. Lett. 106, 118001 (2011):
S. Jaubaud, D. Lohse and D. van der Meer, Phys. Rev. Lett. 108, 210604 (2012):
A. Naert, EPL 97, 20010 (2012):
A. Mounier and A. Naert, EPL 100, 30002 (2012).

2. A. Puglisi, P. Visco, R. Barrat, E. Trizac and F. van Wijland, Phys. Rev. Lett. 95, 11-202 (2005):
A. Puglisi, P. Visco, E. Trizac and F. van Wijland, EPL 72, 55 (2005):
A. Puglisi, P. Visco, E. Trizac and F. van Wijland, Phys. Rev. E 73, 021301 (2006):
A. Puglisi, L. Rondoni, and A. Vulpiani, J. Stat. Mech. (2006) P08001:
A. Sarracino, D. Villamaina, G. Gradenigo and A. Puglisi, EPL 92, 34001 (2010).

3. S.-H. Chong, M. Otsuki and H. Hayakawa, Phys. Rev. E 81, 041130 (2010):
H. Hayakawa, S.-H. Chong and M. Otsuki, in IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flow,
pp.19-30 edited by J. D. Goddard, J. T. Jenkins and P. Govine (AIP vol.1227, New York, 2010):
H. Hayakawa, arXiv: 1303.2311.

4. H. Hayakawa and M. Otsuki, in preparation.
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