A definition of internal constancy and homeostasis in the context of non-equilibrium thermodynamics

The constancy of the internal environment, internal homeostasis, and its stability are necessary conditions for the survival of a biological system within its environment. These have never been clearly defined. For this purpose nonequilibrium thermodynamics is taken as a reference, and the essential principles of equilibrium, reversibility, stationary steady state and stability (Lyapounov, asymptotic, local and global), are briefly illustrated. On this basis, internal homeostasis describes a stationary state of nonequilibrium, the actual state of rest, X(t), resulting from the relation X(t) = Xs + x(t), between a time-independent steady state of reference (Xs), and time-dependent fluctuations of the state variables, x(t). In humans, two resting spontaneous homeostatic states are: (1) the conscious state of quiet wakefulness, during which time-dependent variables display bounded oscillations around the mean time-independent steady state level, this conscious state being thus stable in the sense of Lyapounov, and (2) the unconscious stable state of non-rapid eye movement sleep, in which the time-dependent variables would approach the lowest spontaneously attainable time-independent state asymptotically, sleep becoming a globally stable and attractive state. Exercise may be described as a non-resting, unstable active state far away from equilibrium and hibernation is a resting, time-independent steady state very near equilibrium. The range between sleep and exercise is neurohumorally regulated. For spontaneously stable states to occur, slowing of the metabolic rate, withdrawal of the sympathetic drive and reinforcement of the vagal tone to the heart and circulation are required, thus confirming that the parasympathetic division of the autonomic nervous system is the main controller of homeostasis.