  In this paper, we investigate the thermodynamics of hyperscaling violating
Lifshitz black branes in the presence of a nonlinear massless electromagnetic
field. We, first, obtain analytic nonlinear charged black brane solutions with
hyperscaling violating factor in dilaton gravity and give the condition on the
parameters of the metric for having black brane solutions. Second, we introduce
the appropriate finite action in grand-canonical and canonical ensembles for
nonlinear electromagnetic field. Next, by generalizing the counterterm method
for the asymptotic Lifshitz spacetimes with hyperscaling violating factor, we
calculate the energy density of our solutions. Then, we present a relation
between the energy density and the thermodynamic quantities, electric
potential, charge density, temperature and entropy density. This relation is
the generalization of Smarr formula for anti-de Sitter black branes and charged
Lifshiz solutions. Finally, we perform a stability analysis in both the
canonical and grand-canonical ensemble. We show that the nonlinearity of
electromagnetic field can make the solutions unstable in grand-canonical
ensemble.
