Talmudic discussion of how utensils absorb and release flavors through hot water (hagalah), establishing the principle that heated water causes ta'am to be released from vessel walls — directly relevant to how a dishwasher's hot-water cycle affects absorbed flavors.
תָּנוּ רַבָּנַן: הַלּוֹקֵחַ כְּלֵי תַּשְׁמִישׁ מִן הַגּוֹיִם, דְּבָרִים שֶׁלֹּא נִשְׁתַּמֵּשׁ בָּהֶן — מַטְבִּילָן וְהֵן טְהוֹרִין. דְּבָרִים שֶׁנִּשְׁתַּמֵּשׁ בָּהֶן עַל יְדֵי צוֹנֵן, כְּגוֹן כּוֹסוֹת וְקִתּוֹנִיּוֹת וּצְלוֹחִיּוֹת — מַדִּיחָן וּמַטְבִּילָן וְהֵם טְהוֹרִין. דְּבָרִים שֶׁנִּשְׁתַּמֵּשׁ בָּהֶן עַל יְדֵי חַמִּין, כְּגוֹן הַיּוֹרוֹת הַקּוּמְקְמוֹסִין וּמְחַמֵּי חַמִּין — מַגְעִילָן וּמַטְבִּילָן וְהֵן טְהוֹרִין. דְּבָרִים שֶׁנִּשְׁתַּמֵּשׁ בָּהֶן עַל יְדֵי הָאוּר, כְּגוֹן הַשַּׁפּוּדִין וְהָאַסְכְּלָאוֹת — מְלַבְּנָן וּמַטְבִּילָן וְהֵן טְהוֹרִין. וְכוּלָּן שֶׁנִּשְׁתַּמֵּשׁ בָּהֶן עַד שֶׁלֹּא יַטְבִּיל וְשֶׁלֹּא יַגְעִיל וְשֶׁלֹּא יְלַבֵּן, תָּנֵי חֲדָא: אָסוּר, וְתַנְיָא אִידַּךְ: מוּתָּר. לָא קַשְׁיָא, הָא כְּמַאן דְּאָמַר: נוֹתֵן טַעַם לִפְגָם — אָסוּר, הָא כְּמַאן דְּאָמַר: נוֹתֵן טַעַם לִפְגָם — מוּתָּר.
§ The Sages taught: One who purchases utensils from the gentiles must prepare them for use in the following manner: With regard to items that the gentile did not use, one immerses them, and they are pure. With regard to items that the gentile used for cold food or drink, such as cups and jugs and flasks, one rinses them and immerses them, and they are pure. With regard to items that the gentile used for hot food or drink, such as large pots, small kettles [hakumkamusun], and samovars, one purges them with boiling water and immerses them, and they are pure. With regard to items that the gentile used with fire, such as spits and grills, one heats them until white-hot and immerses them, and they are pure. And with regard to all utensils that one used before immersing and purging and heating them until white-hot, it is taught in one baraita that the food prepared with them is forbidden, and it is taught in another baraita that the food prepared with them is permitted. The Gemara explains: This contradiction is not difficult. This ruling, that the food prepared with such utensils is forbidden, is according to the one who says that if a forbidden substance imparts flavor to a permitted food to the detriment of the mixture, the permitted food is forbidden. That ruling, that the food prepared with such utensils is permitted, is according to the one who says that if a forbidden substance imparts flavor to a permitted food to the detriment of the mixture, it remains permitted. Here too, since the flavor of non-kosher food imparted by the utensil detracts from the flavor of the food, such food is permitted.