It is a very interesting question!
So before everything, it is important to understand what is Temporomandibular joint and its components.
The temporomandibular joints (TMJ) are the two joints connecting the jawbone to the skull. It is a bilateral synovial articulation between the temporal bone of the skull above and the mandible below; it is from these bones that its name is derived. This joint is unique in that it is a bilateral joint that functions as one unit. Since the TMJ is connected to the mandible, the right and left joints must function together and therefore are not independent of each other.
Other components, apart from articular surface of temporal bone and condyle, include various ligaments as well as main and accessory muscles of mastication. Names of all the muscles and ligaments
This image will explain the relationship of TMJ with major masticatory muscle
Many practitioners have speculated that poor posture may have a negative effect on temporomandibular, or TMD, symptoms and treatment outcome.
The most common of them is forward head posture.
With this posture, the head’s center of gravity is forward of the spine’s weight-bearing axis, which increases the strain within the posterior cervical muscles, ligaments and apophyseal joints.
It has been demonstrated that cervical muscle activity influences masticatory muscle activity.Practitioners have theorized that the additional demand that is placed on the posterior cervical region by the forward head posture alters the masticatory system so that people are more susceptible to masticatory muscle strain, spasm and pain.
The guidelines of the American Academy of Orofacial Pain pointed out a correlation of TMD and cervical spine. The cervical spine is intimately related to the cranium and masticatory system via specific joint articulations, muscle attachments, and neural and vascular innervations and the relation of postural balance among them is of fundamental importance to maintain the functionality of the system formed by these structures. Reference
The whole mechanism is beautifully explained in this article-
The biomechanical complexity of body posture derives from the functional integration of several body segments: when there is a change in any biomechanical subunit, a refinement of the postural control systems will necessarily occur. The muscle groups of the stomatognathic system belong to the cervical muscular chain. Considering that the musculoskeletal system is composed of several such muscular chains that are integrated with one another, any disturbance of a body segment will lead to a reorganization of other segments.This fine tuning of posture control leads to body segment adaptation and realignment, whether physically near to or distant from the TMJ.Reference
Also apart from forward head bending this same article aims-
To identify the relationship between anterior disc displacement and global posture (plantar arches, lower limbs, shoulder and pelvic girdle, vertebral spine, head and mandibles)
Note that anterior disc displacement (in which there is clicking heard on opening and/or closing) is a common TMD.
Although it is not possible to positively state a cause-effect relationship, our data at least verify the mutual existence of global body posture deviations and TMD.
Infact, for treatment of TMD there are useful training programs to correct posture. Reference
Concluding I found an interesting image, stating that poor body posture can influence even teeth alignment or the occlusion!
Hope I have satisfactorily answered your question!