  We analytically study the role of nonconservative forces, namely viscous
couplings, on the statistical properties of the energy flux between two
Brownian particles kept at different temperatures. From the dynamical model
describing the system, we identify an energy flow that satisfies a fluctuation
theorem both in the stationary and in transient states. In particular, for the
specific case of a linear nonconservative interaction, we derive an exact
fluctuation theorem that holds for any measurement time in the transient
regime, and which involves the energy flux alone. Moreover, in this regime the
system presents an interesting asymmetry between the hot and cold particles.
The theoretical predictions are in good agreement with the experimental results
already presented in our previous article [B{\'e}rut et al., Phys. Rev. Lett.
116, 068301 (2016)], where we investigated the thermodynamic properties of two
Brownian particles, trapped with optical tweezers, interacting through a
dissipative hydrodynamic coupling.
