Periodic environments and biological oscillations
    
        
            - Day/night
 
            - Tides
 
            - Moon phases
 
            - Cells anticipate periodic environments
 
            - Circadian clocks run without cues (free run). 
 
            - Clocks are entrainable
 
        
    
    
    Nobelprize 2017: Elucidation of the Molecular Mechanisms of Circadian Clocks
    
        
        Jeffrey Hall
     
    
        
        Michael Rosbach
     
    
        
        Michael Young
     
    Images by Nobel media, Nobelprize.org
    
    Physical and biochemical oscillators
    
        
            
                - Pendulum 
$$\frac{d^2\theta(t)}{dt^2} = \frac{g}{L}\sin \theta(t) \approx \frac{g}{L}\theta^2$$  
                - period $$T = 2\pi \sqrt{\frac{g}{L}}$$
 
                - Oscillation driven by back and forth between kinetic and potential energy.
 
            
        
     
    
        
            
                - No equivalent of kinetic energy
 
                - Multi-component systems with interdependent regulation