The second law of thermodynamics implies that no macroscopic system may oscillate indefinitely without consuming energy. This letter places bounds on the degree and quality of such oscillations when the system in question is homogeneous and has discrete states. In a closed system, the maximum number of oscillations is bounded by the system dimension. In open systems, the system size bounds the quality factor of oscillation. This fundamental limit serves as a key design principle for engineered dynamics in chemical systems and nano-scale machines .
The second law of thermodynamics implies that no macroscopic system may oscillate indefinitely without consuming energy. The question of the number of possible oscillations and the coherent quality of those oscillations remain unanswered. This paper proves the upper-bounds on the number and quality of such oscillations when the system in question is homogeneously driven and has discrete states. In a closed system, the maximum number of oscillations is bounded by the system dimension. In open systems, the system size bounds the quality factor of oscillation. I also prove that homogeneously driven systems with discrete states must have a loop topology to allow oscillations. The consequences of this limit are explored in the context of chemical clocks and limit cycles .
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This letter places bounds on the degree
The question of the number of possible oscillations and the coherent quality of those oscillations remain unanswered. This paper proves the upper-bounds on the number
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homogeneous
homogeneously driven
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This fundamental limit serves as a key design principle for engineered dynamics in chemical systems and nano-scale machines
I also prove that homogeneously driven systems with discrete states must have a loop topology to allow oscillations. The consequences of this limit are explored in the context of chemical clocks and limit cycles