When indicating something processes slowly and gradually, we can use 渐渐, 慢慢 and 逐渐.
e.g.
太阳渐渐/慢慢/逐渐落山了。(Tàiyánɡ jiànjiàn / mànmàn / zhújiàn luò shān le.) The sun went down gradually.
刚开始我不习惯这里的吃的,现在我渐渐/慢慢/逐渐习惯了。(Gānɡ kāishǐ wǒ bù xíɡuàn zhèlǐ de chide, xiànzài wǒ jiànjiàn / mànmàn / zhújiàn xíɡuàn le.) I wasn’t accustomed to the food here, but now I’m used to it gradually.
逐渐and 渐渐 are almost the same. They are both adverbs which can be used to indicate a change happened gradually, by degrees. 渐渐 is more informal than 逐渐, in other words, 逐渐 often for written and formal situations while 渐渐 often for oral and informal ones.
“gradually”
逐渐 / 渐渐 + Verb / Adjective
e.g.
天逐渐/渐渐黑了下来。(Tiān zhújiàn / jiànjiàn hēile xiàlái.) It became dark gradually.
他的汉语口语正在逐渐/渐渐变好。(Tā de Hànyǔ kǒuyǔ zhènɡzài zhújiàn / jiànjiàn biàn hǎo.) His spoken Chinese is becoming better gradually.
慢慢as an adverb indicates “slowly” that describes an action or a state progresses in a slow and continuous speed.
慢慢 + Verb / Adejective
e.g.
你慢慢吃,别急!(Nǐ mànmàn chī, bié jí!) You eat slowly, don’t be hurried!
你听我慢慢跟你说。(Nǐ tīnɡ wǒ mànmàn ɡēn nǐ shuō.) Let me tell you slowly.
他的脸慢慢红了起来。(Tā de liǎn mànmàn hónɡle qǐlái.)
慢慢 means “slowly” which stresses the action or state done in a slow speed while 渐渐 means “gradually” which emphasizes something changed little by little undetectably. Actually, almost all situation for 渐渐, 慢慢 can still be used but in a slight different meaning.
e.g.
雨渐渐/慢慢变大了。(Yǔ jiànjiàn / mànmàn biàn dà le.) The rain is becoming heavy gradually / slowly.
>> 渐渐 indicates the rain becomes heavy gradually, little by little.
>> 慢慢 indicates the rain becomes heavy slowly, not hurriedly.
还有时间,慢慢写!(Háiyǒu shíjiān, mànmàn xiě!) There is still some time, so take your time to write!
✘ 还有时间,渐渐写!
渐渐 mainly modify nonvolitional verbs as an adverbial in a statement sentence only. But慢慢 has no limits which can modify both volitional verbs like “说” “吃” “喝” “睡觉” “走路” etc. and nonvolitional verbs like “了解” “知道” “想” “饿” “病” etc. to serve as an adverbial in a statement or an imperative sentence.
e.g.
他慢慢/渐渐听明白了。(Tā mànmàn / jiànjiàn tīnɡ mínɡbɑi le.) He understands slowly / gradually.
>> 听明白 is a result which is more like a state not an action, so 慢慢 and 渐渐 are both fine.
你慢慢做饭。(Nǐ mànmàn zuò fàn.) Take your time to make a meal.
✘ 你渐渐做饭。
>> 做饭 is a verbal phrase indicating an action, so we use 慢慢.
Beside as an adverbial, 慢慢 can also be an attributive or predicate in a sentence while 渐渐 can’t.
e.g.
他说话总是慢慢的。(Tā shuōhuà zǒnɡshì mànmàn de.) He always talks slowly.
✘ 他说话总是渐渐的。
>> 慢慢 here serves as a predicate.
他做事就是这种慢慢的风格。(Tā zuò shì jiùshì zhè zhǒnɡ mànmànde fēnɡɡé.) Doing things slowly is his style.
✘ 他做事就是这种渐渐的风格。
>> 慢慢 here serves as an attributive.
别跑,慢慢走!(Bié pǎo, mànmàn zǒu!) Not run, just walk slowly!
✘ 别跑,渐渐走!
>> 走 is an action word, so we need 慢慢 instead of 渐渐.
逐步 as an adverb can indicate an action or a state changed step by step intentionally and prepensely by people or organizations.
“step by step”
逐步 + Verb
e.g.
我们要逐步完善我们的计划。(Wǒmen yào zhúbù wánshàn women de jìhuà.) We need to polish up our plan step by step.
>> To stress the plan will be done step by step
要逐步提高他们的汉语水平。(Yào zhúbù tíɡāo tāmen de Hànyǔ shuǐpínɡ.) It’s necessary to improve their level of Chinese language.
>> To stress this thing need to be done step by step.
For 逐步 and 逐渐, they are both adverbs, so they can be functioned as an adverbial before the verb. Besides verb, 逐渐 can also modify an adjective while 逐步 can’t.
e.g.
他逐渐忘了这件事。(Tā zhújiàn wànɡle zhè jiàn shì.) He forgot it gradually.
天气逐渐暖和起来了。(Tiānqì zhújiàn nuǎnhuo qǐlái le.) It becomes warm gradually.
我们逐步解决这个问题。(Wǒmen zhúbù jiějué zhèɡe wèntí.) We will solve this problem step by step.
When emphasizing a change happened little by little, naturally and undesignedly, 逐渐 should be used. While if it is occurred step by step, designedly and progressively by a person or an organization, 逐步 should be applied.
e.g.
他们正在逐步/逐渐采取新措施。(Tāmen zhènɡzài zhúbù / zhújiàn cáiqǔ xīn cuòshī.)
They are taking new measures step by step / gradually.
>> 逐步 stresses these measures are done step by step. And there are obvious stages.
>> 逐渐 focuses on the change happened little by little.
来这里的人逐渐多了起来。(Lái zhèlǐ de rén zhújiàn duōle qǐlái.) There are more and more people coming here gradually.
✘ 来这里的人逐步多了起来。
新博物馆将逐步对外开放。(Xīn bówùɡuǎn jiānɡ zhúbù duì wài kāifànɡ.) The new museum will open gradually.
✘ 新博物馆将逐渐对外开放。
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