D. Bakry, P. Cattiaux, and A. Guillin, Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré, J. Funct. Anal, vol.254, issue.3, pp.727-759, 2008.

V. Bansaye, B. Cloez, and P. Gabriel, Ergodic behavior of nonconservative semigroups via generalized doeblin's conditions, 2017.

A. Bensoussan, J. L. Lions, and G. C. Papanicolaou, Boundary layers and homogenization of transport processes, Publ. Res. Inst. Math. Sci, vol.15, issue.1, pp.53-157, 1979.

G. Peter, J. L. Bergmann, and . Lebowitz, New approach to nonequilibrium processes, Phys. Rev, vol.99, issue.2, pp.578-587, 1955.

E. Bernard and F. Salvarani, On the exponential decay to equilibrium of the degenerate linear Boltzmann equation, J. Funct. Anal, vol.265, issue.9, pp.1934-1954, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00724613

M. Bisi, J. A. Cañizo, and B. Lods, Entropy dissipation estimates for the linear Boltzmann operator, J. Funct. Anal, vol.269, issue.4, pp.1028-1069, 2015.

M. Briant, Instantaneous exponential lower bound for solutions to the Boltzmann equation with Maxwellian diffusion boundary conditions, Kinet. Relat. Models, vol.8, issue.2, pp.281-308, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01492036

M. Briant, Instantaneous filling of the vacuum for the full Boltzmann equation in convex domains, Arch. Ration. Mech. Anal, vol.218, issue.2, pp.985-1041, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01492021

A. José, J. A. Cañizo, S. Carrillo, and . Cuadrado, Measure Solutions for Some Models in Population Dynamics, Acta Applicandae Mathematicae, vol.123, issue.1, pp.141-156, 2013.

A. José, A. Cañizo, B. Einav, and . Lods, On the rate of convergence to equilibrium for the linear boltzmann equation with soft potentials, 2017.

M. J. Cáceres, J. A. Carrillo, and T. Goudon, Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles, Comm. Partial Differential Equations, vol.28, issue.5-6, pp.969-989, 2003.

A. José, H. Cañizo, and . Yolda?, Asymptotic behaviour of neuron population models structured by elapsed-time, Nonlinearity, vol.32, issue.2, p.464, 2019.

C. Cao, The kinetic Fokker-Planck equation with weak confinement force, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01697058

E. A. Carlen, R. Esposito, J. L. Lebowitz, R. Marra, and C. Mouhot, Approach to the steady state in kinetic models with thermal reservoirs at different temperatures, 2016.

P. Cattiaux and A. Guillin, Functional inequalities via Lyapunov conditions, Optimal transportation, vol.413, pp.274-287, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00446104

L. Desvillettes and C. Villani, On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: the linear Fokker-Planck equation, Comm. Pure Appl. Math, vol.54, issue.1, pp.1-42, 2001.

L. Desvillettes and C. Villani, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation, Invent. Math, vol.159, issue.2, pp.245-316, 2005.

J. Dolbeault, C. Mouhot, and C. Schmeiser, Hypocoercivity for linear kinetic equations conserving mass, Trans. Amer. Math. Soc, vol.367, issue.6, pp.3807-3828, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00482286

R. Douc, G. Fort, and A. Guillin, Subgeometric rates of convergence of f -ergodic strong Markov processes, Stochastic Process. Appl, vol.119, issue.3, pp.897-923, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00077681

G. Dumont and P. Gabriel, The mean-field equation of a leaky integrateand-fire neural network: measure solutions and steady states, 2017.

E. Weinan and D. Li, The Andersen thermostat in molecular dynamics, Comm. on Pure and App. Math, vol.61, issue.1, pp.96-136, 2010.

J. Evans, Hypocoercivity in Phi-entropy for the Linear Relaxation Boltzmann Equation on the Torus, 2017.

N. Fournier and S. Méléard, A Markov process associated with a Boltzmann equation without cutoff and for non-Maxwell molecules, J. Statist. Phys, vol.104, issue.1-2, pp.359-385, 2001.

P. Gabriel, Measure solutions to the conservative renewal equation, ESAIM: ProcS, vol.62, pp.68-78, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01500471

M. P. Gualdani, S. Mischler, and C. Mouhot, Factorization for non-symmetric operators and exponential H-theorem, vol.153, 2018.
URL : https://hal.archives-ouvertes.fr/hal-00495786

M. Hairer, Lecture notes: P@w course on the convergence of markov processes, 2016.

M. Hairer and J. C. Mattingly, Yet another look at Harris' ergodic theorem for Markov chains, Seminar on Stochastic Analysis, Random Fields and Applications VI, vol.63, pp.109-117, 2011.

T. E. Harris, The existence of stationary measures for certain Markov processes, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol.II, pp.113-124, 1954.

F. Hérau, Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation, Asymptot. Anal, vol.46, issue.3-4, pp.349-359, 2006.

F. Hérau and F. Nier, Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential, Arch. Ration. Mech. Anal, vol.171, issue.2, pp.151-218, 2004.

J. L. Lebowitz and P. G. Bergmann, Irreversible Gibbsian ensembles, Ann. Physics, vol.1, pp.1-23, 1957.

B. Lods and M. Mokhtar-kharroubi, Convergence to equilibrium for linear spatially homogeneous Boltzmann equation with hard and soft potentials: a semigroup approach in L 1 -spaces, Math. Methods Appl. Sci, vol.40, issue.18, pp.6527-6555, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01213416

B. Lods, C. Mouhot, and G. Toscani, Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models. Kinetic and Related Models, vol.1, pp.223-248, 2008.

J. C. Mattingly, A. M. Stuart, and D. J. Higham, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Process. Appl, vol.101, issue.2, pp.185-232, 2002.

P. Sean, R. L. Meyn, and . Tweedie, Markov chains and stochastic stability, Communications and Control Engineering Series, 1993.

M. Mokhtar-kharroubi, On L 1 exponential trend to equilibrium for conservative linear kinetic equations on the torus, J. Funct. Anal, vol.266, issue.11, pp.6418-6455, 2014.

C. Mouhot, Quantitative lower bounds for the full Boltzmann equation. I. Periodic boundary conditions, Comm. Partial Differential Equations, vol.30, issue.4-6, pp.881-917, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00087249

C. Mouhot and L. Neumann, Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus, Nonlinearity, vol.19, issue.4, pp.969-998, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00087173

C. Villani, Hypocoercivity. Mem. Amer. Math. Soc, vol.202, issue.950, p.141, 2009.