This is an important question with many possible answers.

A very good place to start in answering this question is

https://www.researchgate.net/topic/Quantum-Statistical-Mechanics

See, for example:

https://www.researchgate.net/publication/309466935_The_role_of_curvature_in_quantum_statistical_mechanics

and

https://www.researchgate.net/publication/309207515_Statistical_mechanics_approach_to_lattice_field_theory

For very recent research in statistical mechanics, see

Wei Nie, Feng Mei, Luigi Amico, Leong Chuan Kwek

Scaling of geometric phase close to multicritical points in cluster-Ising models

https://arxiv.org/abs/1702.02501

and

Dipanjan Mandal, Trisha Nath, R. Rajesh

Estimating the Critical Parameters of the Hard Square Lattice Gas Model

https://arxiv.org/abs/1702.02332

Tianfu Gao, Zhigang Zheng, Jincan Chen

Resonant current in coupled inertial Brownian particles with delayed-feedback control

https://arxiv.org/abs/1702.02318

Article The role of curvature in quantum statistical mechanics

Article Statistical mechanics approach to lattice field theory

This is an important question with many possible answers.

A very good place to start in answering this question is

https://www.researchgate.net/topic/Quantum-Statistical-Mechanics

See, for example:

https://www.researchgate.net/publication/309466935_The_role_of_curvature_in_quantum_statistical_mechanics

and

https://www.researchgate.net/publication/309207515_Statistical_mechanics_approach_to_lattice_field_theory

For very recent research in statistical mechanics, see

Wei Nie, Feng Mei, Luigi Amico, Leong Chuan Kwek

Scaling of geometric phase close to multicritical points in cluster-Ising models

https://arxiv.org/abs/1702.02501

and

Dipanjan Mandal, Trisha Nath, R. Rajesh

Estimating the Critical Parameters of the Hard Square Lattice Gas Model

https://arxiv.org/abs/1702.02332

Tianfu Gao, Zhigang Zheng, Jincan Chen

Resonant current in coupled inertial Brownian particles with delayed-feedback control

https://arxiv.org/abs/1702.02318

Article The role of curvature in quantum statistical mechanics

Article Statistical mechanics approach to lattice field theory

Thankful for your answers Mr. Peters and Mr. Kralj

I understand that it is a question with many possible answers. I have seen that much of the research is geared towards complex systems in chemistry and biology. I believe that the benefits of scientific computing technologies have greatly facilitated this trend. Statistical thermodynamics also I think plays an important role.

Regards ,

Ender Araujo

See also the 2014 video linked below:

https://video.ias.edu/nedrm/2014/0328-DavidHuse