  The present work is devoted to explore some interesting cosmological features
of a newly proposed theory of gravity namely $\mathcal{F}(R,L_m,T)$ theory,
where $R$ and $T$ represent the Ricci scalar and trace of energy
momentum-tensor, respectively. Firstly, a non-equilibrium thermodynamical
description is considered on the apparent horizon of the Friedmann's cosmos.
The Friedmann equations are demonstrated to be equivalent to the first law of
thermodynamics, i.e.,
${T_{Ah}d\varepsilon_{h}^\prime+T_{Ah}d_{i}\varepsilon_{h}^\prime=-d\hat{E}+\hat{W}dV}$,
where ${d_{i}\varepsilon_{h}^\prime}$ refers to entropy production term. We
also formulate the constraint for validity of generalized second law of
thermodynamics and check it for some simple well-known forms of generic
function $\mathcal{F}(R,L_m,T)$. Next, we develop the energy bounds for this
framework and constraint the free variables by finding the validity regions for
NEC and WEC. Further, we reconstruct some interesting cosmological solutions
namely power law, $\Lambda$CDM and de Sitter models in this theory. The
reconstructed solutions are then examined by checking the validity of GSLT and
energy bounds. Lastly, we analyze the stability of all reconstructed solutions
by introducing suitable perturbations in the field equations. It is concluded
that obtained solutions are stable and cosmologically viable.
