Fluctuations Beyond Detailed Balance in Voltage-Gated Channels

To survive, living systems interact with and adapt to their fluctuating environments. In the process they must maintain homeostasis, which supports the thermodynamic conditions for internal biochemical and metabolic processing. We show how to separate this thermodynamic behavior into two pieces. The first is "homeostatic"---associated with maintaining nonequilibrium steady states. The second is "adaptive"---energy required as a system attempts to relax to its steady states. The theory culminates in a nonequilibrium steady-state trajectory class fluctuation theorem, valid for a broad class of mesoscopic complex systems. We apply this to directly compare the energetic behavior of the sodium and potassium ion channels responsible for generating and propagating signals in mammalian neurons. We explore how one of the channels violates detailed balance while the other does not, driving both of them with a biologically-plausible action potential spike. This uncovers new quantitative structures that facilitate how nonequilibrium steady-state systems function while necessarily violating detailed-balanced thermodynamics. This mechanism leverages an "extra dimension" of Second Law violations accessible only to nondetailed-balanced systems---dimensions that must be thermodynamically accounted for. Practically, our results point towards necessary procedures for experimentally probing how complex biological systems absorb and dissipate energy.