2010/06/02 by Nathan O. Hodas, Hodas, Nathan O.
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · #60J27 #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Mathematical Physics (math-ph) #Molecular Junctions and Nanostructures #Molecular Networks (q-bio.MN) #Pattern Formation and Solitons (nlin.PS) #Social and Information Networks (cs.SI) #Spectral Theory (math.SP) #Statistical Mechanics (cond-mat.stat-mech) #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.1006.0271
openalex publication_date 2010/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 these 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 a discrete network of states. In a closed system, the maximum number of oscillations is bounded by the number of states in the network. In open systems, the size of the network bounds the quality factor of oscillation. This work also explores how the quality factor of macrostate oscillations, such as would be observed in chemical reactions, are bounded by the smallest equivalent loop of the network, not the size of the entire system. The consequences of this limit are explored in the context of chemical clocks and limit cycles.