  A living non-Newtonian matter like the cell cortex and tissues are driven
out-of-equilibrium at multiple spatial and temporal scales. The stochastic
dynamics of a particle embedded in such a medium are non-Markovian, given by a
generalized Langevin equation. Due to the non-Markovian nature of the dynamics,
the heat dissipation and the entropy production rate cannot be computed using
the standard methods for Markovian processes. In this work, to calculate heat
dissipation, we use an effective Markov description of the non-Markovian
dynamics, which includes the degrees-of-freedom of the medium. Specifically, we
calculate entropy production and heat dissipation rate for a spherical colloid
in a non-Newtonian medium whose rheology is given by a Maxwell viscoelastic
element in parallel with a viscous fluid element, connected to different
temperature baths. This problem is nonequilibrium for two reasons: the medium
is nonequilibrium due to different effective temperatures of the bath, and the
particle is driven out-of-equilibrium by an external stochastic force. When the
medium is nonequilibrium, the effective non-Markov dynamics of the particle may
lead to a negative value of heat dissipation and entropy production rate. The
positivity is restored when the medium's degree-of-freedom is considered. When
the medium is at equilibrium, and the only nonequilibrium component is the
external driving, the correct dissipation is obtained from the effective
description of the particle.
