Capsaicin, the active component in chili peppers, has been extensively studied for its analgesic properties, particularly in alleviating nerve, muscle, and joint pain. Its efficacy is primarily attributed to its interaction with the transient receptor potential vanilloid 1 (TRPV1) receptor, leading to desensitization of pain fibers and subsequent pain relief.

Neuropathic Pain:

A systematic review published in The BMJ analyzed randomized controlled trials assessing the effectiveness of topical capsaicin in chronic pain management. The review found that capsaicin provided moderate pain relief in conditions like postherpetic neuralgia and diabetic neuropathy, with a number needed to treat (NNT) of 5.7, indicating its potential as a therapeutic agent for neuropathic pain. 

https://www.bmj.com/content/328/7446/991

Musculoskeletal Pain:

The same BMJ review also evaluated capsaicin's efficacy in musculoskeletal disorders, including osteoarthritis and rheumatoid arthritis. The findings suggested a modest benefit, with an NNT of 8.1, highlighting that while capsaicin can be effective, its benefits may be limited in musculoskeletal pain compared to neuropathic conditions. 

Mechanism of Action:

Research from Rutgers University has provided insights into the analgesic mechanisms of capsaicin. Studies indicate that capsaicin activates TRPV1 receptors on sensory neurons, leading to an influx of calcium ions. This activation results in the depletion of phosphoinositides, which in turn inhibits mechanically activated ion channels like Piezo1 and Piezo2, crucial for transmitting mechanical pain. This pathway elucidates how capsaicin can alleviate various pain types, including those originating from nerves, muscles, and joints. 

https://www.rutgers.edu/news/rutgers-researchers-uncover-pain-relief-secrets-hot-chili-peppers

Clinical Applications:

Topical formulations of capsaicin, such as creams and patches, have been developed for clinical use. A high-concentration capsaicin 8% patch (Qutenza™) has been approved in the EU and USA for managing neuropathic pain. A single 60-minute application can provide pain relief for several weeks, offering a convenient option for patients. 

https://www.bjanaesthesia.org/article/S0007-0912%2817%2933029-5/fulltext

Safety and Adverse Effects:

While capsaicin is generally considered safe, common adverse effects include localized burning, stinging, and erythema at the application site. These side effects are typically transient and diminish with continued use. Systemic adverse events are rare due to minimal systemic absorption. 

In summary, capsaicin has demonstrated efficacy in relieving nerve, muscle, and joint pain, with a well-elucidated mechanism of action involving TRPV1 receptor activation and subsequent modulation of pain pathways. Its clinical applications, particularly in neuropathic pain, are supported by evidence from systematic reviews and clinical studies. However, its effectiveness in musculoskeletal pain appears to be more modest, and patients should be informed about potential local adverse effects.