Does turmeric help reduce inflammation and does cayenne improve circulation? How do these responses occur?
A lack of space forces me to approach only the topic of turmeric here.
"Uncontrolled inflammation plays a role in many major diseases, including cancer, heart disease, diabetes and Alzheimer's disease" (Science Daily, May 16, 2016, https://www.sciencedaily.com/releases/2016/05/160516091547.htm ).
Studies show that the ancient spice turmeric, as well as its component called curcumin, have anti-inflammatory properties.
The University of Maryland Medical Center tells us (https://www.umm.edu/health/medical/altmed/herb/turmeric ) that "Turmeric has been used in both Ayurvedic and Chinese medicine as an anti-inflammatory, to treat digestive and liver problems, skin diseases, and wounds. Curcumin is also a powerful antioxidant".
While both -- the Ayurvedic and Chinese forms of medicine -- are thousands of years old, contemporary university studies confirm some of this information transmitted to us.
"Extensive clinical trials over the past quarter century have addressed the pharmacokinetics, safety, and efficacy of this nutraceutical [curcumin] against numerous diseases in humans.
Some promising effects have been observed in patients with various pro-inflammatory diseases" (Therapeutic Roles of Curcumin: Lessons Learned from Clinical Trials, AAPS J. 2013 Jan; 15(1): 195–218. DOI: 10.1208/s12248-012-9432-8 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3535097/).
The mechanism of action comes from its ability to bring back to normal "numerous signaling molecules such as pro-inflammatory cytokines, apoptotic proteins, NF–κB [...], C-reactive protein, [...] prostate-specific antigen, [...] triglyceride, [etc], in human participants" (see above link).
However, only some types of turmeric as a nutraceutical are very well absorbed in humans (depending on brand) and one has to carefully investigate descriptions and reviews.
Cooking a delicious Indian curry dish might also be a good choice.