In his treatise, HaKafe v'haMitzvot, R. Aaron Schuman writes: It was revealed at Mount Sinai that Hashem ordained that heat shall flow from hotter regions to colder. This revelation was preserved as a secret teaching until R Josiah Gibbowitz (z"l) inscribed it as Hashem's 2nd Commandment of Thermodynamics. There is a little known mitzvah, "Thou shalt never stir the cream into thy morning coffee; thereby shall you observe convection currents and remember My second commandment of thermodynamics." (Since this is a time-bound mitzvah, women are exempt.) The parenthetical remark seemed incorrect, a little further research uncovers a rich tradition of Jewish law brewing around this allegedly "secret teaching."
Even if we understand that this mitzvah only applies to coffee drunk in the morning, women are only exempt from mitzvot aseh shehazman grama [time-bound commandments phrased as "thou shalt"], whereas this is a mitzvat lo taaseh [phrased as "thou shalt not"]. Therefore we conclude that women are equally bound to contemplate convection currents. R. Chama bar Karkar argues that this mitzvah is not really time-bound at all. What if one only drinks coffee after supper? The mitzvah applies to kos rishon (the first cup of coffee in each day), whether drunk in the morning, afternoon or evening. Some delay drinking kos rishon until later in the day, when they have more time to observe the swirling patterns at greater length. Do we not pray in the Amida: "v tovotecha shebehol eyt, erev vavoker vatzohoraim" [(we thank you...) for your goodness at all times evening, morning and afternoon]? And is not coffee with cream one of G-d's goodnesses? Therefore our sages maintain that this mitzvah applies to coffee drunk at any time, not only kos rishon. (Halacha follows this opinion.) Once again, women and men are both obligated in this mitzvah. Are Jews, then, commanded to drink coffee? No, but those who do are considered praiseworthy. What of those who do not drink coffee? They are obligated to contemplate the coffee of a friend, and to refrain from stirring it (masechet Shotah, perek Shtayim Shotim B'kos, mishnah kaf-he). May one contemplate the coffee of a non-Jew? Rambam notes that coffee has never been used in avodah zarah [idol worship], so one may contemplate it. The RiTzPa notes that one may not drink it unless it was prepared and served in kosher vessels, but one may contemplate it even in unkosher vessels. Later commentators note that Ashkenazim do not do this, and Sephardim only do it when it will annoy Ashkenazim. May one prepare the coffee, refrain from stirring, yet not drink? Bet Hillel say that such a person is yotze, as long as one observes the convection currents and remembers the 2nd Commandment of Thermodynamics. Bet Shammai say that one must drink as well. (As usual, we follow Bet Hillel.) Rashi comments that although one need not drink the coffee, the coffee must not be wasted, lest we transgress bal tashchit [do not destroy]. What of coffee drunk following a meat meal? Since real cream is forbidden in this circumstance, may one observe the mitzvah with pareve ersatz cream? Rambam says no, since the principle of hiddur mitzvah [beautifying a commandment] demands that we use the tastiest ingredients we can afford, and mocha mix is inferior to authentic cream. Hence we do not serve coffee after meat. (Black coffee does not fulfill the mizvah.) Mishnah Brewrah notes that those who are especially pious refrain from eating meat at any time so that they will always be ready to observe this mitzvah with real cream. So important is real cream that even skim milk is unacceptable (except for those with certain medical conditions). Concerning hiddur mitzvah, the Kos Tam (R. Yuban Chockfullanussen) argues that in addition to fine quality coffee and cream, one must also use fine implements. Not only must the coffee be served in a delicate cup (with a saucer!), but when one refrains from stirring, one must refrain from stirring with a silver spoon. To refrain with a wooden or plastic stick, when a fine spoon was available, shows disrespect for the Torah and brings disgrace on one's family.
One should take care to avoid spilling any coffee on the unused stirring implement, so that nobody will see it and conclude (erroneously) that stirring is permissible. Likewise, although one may first stir sugar into coffee and then refrain from stirring after adding cream, those who are strict do not do this, to avoid wetting the stirrer. Neither may one stir the coffee first, and then pour in cream while the coffee is still in motion relying on turbulence to mix the cream. The Torah is explicit that the purpose is to observe convection currents (which must be generated by temperature diffential, and not any other motion or current). In recent years it has become common to use special coffee cups made of glass, so that one may observe the currents not only from the top, but from the sides and bottom as well. Harei zeh mishubach, although we do not invalidate cups made of fine china.