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I have been using a laptop with 2.3 GHz processor clock speed so far, which has been sufficient for my needs (which peak at some intensive programming, e.g. ML).

I'm looking for a new one right now, and saw a laptop advertised as having "1.0 GHz, up to 3.6 GHz with Turbo boost".

I have no idea how Turbo Boost works. I don't understand what it means for the processor to automatically ramp up its speed when intensive programs are running -- as far as I can tell, any program would work better with a higher processing speed.

(When) can I expect 3.6 GHz performance from this CPU? Or will it be more like running a laptop on battery saving mode?

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1GHz is the guaranteed worst case.

My laptop is 1.3GHz but boosts up to 3.6GHz and under load floats somewhere around 2.4-2.8GHz.

It all depends on ambient temperature, heatsink, other heat sources such as battery charging (which causes heat) fans, power usage and other things.

You'll get the "full" boost speed on small bursty single-core tasks and somewhere between the "normal" 1GHz and full boost speed during normal operation.

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"Turbo boost" is explicitly UP TO. Especially in laptops it's not guaranteed that your CPU will ever reach that speed (for more than a fraction of a second at a time, at least). Much depends on how well the laptop's design can keep the CPU cool and how the motherboard manages the performance. Without knowing the specific laptop(and the applicable power saving settings you enable/disable in both the operating system and the BIOS), it's not possible to say much more - the CPU could spend most of the time under load operating at 1GHz with single-core boost never reaching 3.6GHz, or closer to 3GHz with single-core boost frequently capping at 3.6GHz(though in the latter case, don't expect much from the battery).

Do note, that I said single-core when referring to 3.6GHz. With the way Intel's nomenclature and turbo-boost algorithms work, the maximum turbo frequency only applies when one core is under heavy load and the other cores are (mostly) idle.

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