Skipping over a few mathematical steps the probability of electron transfer can be calculated (albeit quite difficult) using the following formula

With 
  
    
      
        J
      
    
    {\displaystyle J}
   being the electronic coupling constant describing the interaction between the two states (reactants and products) and 
  
    
      
        g
        (
        t
        )
      
    
    {\displaystyle g(t)}
   being the line shape function. Taking the classical limit of this expression, meaning 
  
    
      
        ℏ
        ω
        ≪
        k
        T
      
    
    {\displaystyle \hbar \omega \ll kT}
  , and making some substitution an expression is obtained very similar to the classically derived formula, as expected.
The term γ inside the logarithm is the activity and x is the ratio of the ion to the total composition of the electrode. The novel term Ω is the partial molar volume of the ion in the host and σ corresponds to the mean stress felt by the system. The result of this equation is that diffusion, which is dependent on chemical potential, gets impacted by the added stress and, therefore changes the battery’s performance. Furthermore, mechanical stresses may also impact the electrode’s solid-electrolyte-interphase layer. The interface which regulates the ion and charge transfer and can be degraded by stress. Thus, more ions in the solution will be consumed to reform it, diminishing the overall efficiency of the system. Other anodes and cathodes
In a vacuum tube or a semiconductor having polarity (diodes, electrolytic capacitors) the anode is the positive (+) electrode and the cathode the negative (−). The electrons enter the device through the cathode and exit the device through the anode. Many devices have other electrodes to control operation, e.g., base, gate, control grid. In a three-electrode cell, a counter electrode, also called an auxiliary electrode, is used only to make a connection to the electrolyte so that a current can be applied to the working electrode. The counter electrode is usually made of an inert material, such as a noble metal or graphite, to keep it from dissolving. Welding electrodes
In arc welding, an electrode is used to conduct current through a workpiece to fuse two pieces together.