A "hierarchical system" in the long temporal scheme are open to the exchange of matter and energy with the environment, but that within the smaller evolution windows, in which a subsystem is considered to be surrounded by an isothermal, isobaric thermostat, are considered as thermodynamically closed and hence applicable to classical thermodynamic analysis.  This branch of thermodynamics was founded by Russian physical chemist Georgi Gladyshev in 1978. 
Each hierarchical system determined, in this point of view, represents a set of subordinate subsystems related hierarchically by their positions in space, i.e. structurally, or in spatial hierarchy, and or in time, i.e. in a time hierarchy. The central notion in hierarchical thermodynamics, is the conception of the "partial evolution" of the i-th process, i.e. the aggregation of the k-th components of the system participating in process i on level j.
Hierarchical thermodynamics is a generalized theory which may be applied to systems that are characterized by the functions of states. These functions have full differentials and, to within a good approximation, at any moment of time, in quasi-closed mono-hierarchical systems have a real physical meaning, i.e. a quantitative sense.  The outline of hierarchical thermodynamics, in a general sense, can be summarized by the following dictum:
The hierarchical thermodynamics is a linear kinetic thermodynamics of near to equilibrium systems in which variations in the functions of state over time occur. The hierarchical thermodynamics was created on the 19-th century foundation of the exact physicochemical theories of American mathematical physicist Willard Gibbs. Hierarchical thermodynamics is a further development of Gibbsian theory and to within a known approximation is applied to systems of all temporal (structural) hierarchies of real world.
Especial interest is the application of hierarchical thermodynamics to living systems which, as before believed, could not be investigated by Gibbsian methods. The reason of this was the statement that natural biological systems are open and that these systems are, allegedly, far from an equilibrium state.
Recently, however, the law of temporal hierarchies was formulated. This law substantiates the possibility of identifying, or discerning, quasi-closed mono-hierarchical systems or subsystems within open poly-hierarchical biological systems. It was also established, as a rule, that the processes of evolution in living natural systems are quasi-equilibrium processes. It was shown that models of living systems are analogues of models of equilibrium or quasi-equilibrium chromatographic columns. In recent years, hierarchical thermodynamics has found applications in areas such as anti-aging and human chemistry. 
Hierarchies in evolutionary open systems
A general difficulty in the application of classical thermodynamics to the modeling of the evolutionary dynamics of biospheric systems is the “openness” of the systems. In any given volumetric region of the earth, such as cubic meter of region attached to any random latitude, longitude and distance from the earth’s center, atoms will tend to cycle or move through the region according to various biogeochemical reactions at turnover rates ranging from one day to 10,000 days.  In one sense, then, biospheric systems can be considered as volumetric regions through which mass flows due to biogeochemical heat actions. This type of systems view is difficult to analyze from a thermodynamic perspective.
In considering smaller time-defined compartmentalized regions, e.g. an ecological niche during a growing season, however, thermodynamic analysis becomes more intuitive. Gladyshev realized this and, beginning in the late 1970s, developed a means to find such systems based on a criterion of constant “surroundings” or thermostat. In this mode, evolutionary biogeochemical systems can be seen according their relative hierarchies to each other. In this view of logic, a number of conclusions can be drawn, as were outlined in detail by Gladyshev in his 1988 book Thermodynamics and Macrokinetics of Natural Hierarchical Processes, written in Russian. This basic conclusions, which form the structure of “hierarchical thermodynamics”, were peer-reviewed by the late English chemical engineer Kenneth Denbigh. Those conclusions are:
1. Whether current quasi-equilibria, that might be characterized in terms of the corresponding thermodynamic function extremum values, may be established in evolutionary open systems?
2. Whether quasi-closed type subsystems may be singled out from open hierarchical systems allowing the study, in appropriate time scales, of the behavior and evolution of the subsystems using thermodynamic functions with extremum properties?
3. Whether behavior and evolution of open non-stationary systems can be studied using mean specific values of classical thermodynamic function tending to extremum?
The answers to the first two questions, according to Gladyshev, are trivial and can be provided on the basis of the generally known concepts. The third question appears to be a new one and can be answered positively when the open system under consideration is in a thermostat, together with which it presents a complete thermodynamic system. The totality of the environment (thermostat) and a living organism (an open non-stationary system per se) furnishes an example of such complete system. Primarily, the non-stationary open system under consideration is not in equilibrium with its thermostat; its evolution is explained in terms of the tendency to extremum of the mean specific value corresponding to the classic thermodynamic potential of the system formation. The system evolution is directed towards a new partial system state, namely that correspondent to the thermostat equilibrium. In the case of biological systems, it is convenient to use mean specific values of the Gibbs function related to a unit of volume or mass, such as:
This could represent, for example, the mean specific value of the Gibbs function for intermolecular interactions at formation of supramolecular structure of an organism’s biotissue j. It has been show, according to Gladyshev, that in the case when there is a thermostat which provides constancy of the environment’s chemical composition the volumetric Gibbs free energy volume of subsystem:
of an open biosystem j has the tendency to a minimum. This trend of the volumetric Gibbs free energy to a minimum, according to Gladyshev, explains the accumulation of substance with chemically high energy capacity by the biosystem which causes increase in the mean specific chemical component:
of the biological structure during long periods of evolution. The constructiveness of this new concept is evident because it focuses on the investigation of the open non-stationary system characteristics per se. This is very attractive because it offers the possibility of obtaining important quantitative information on the basis of experimental data. This approach has enabled us to substantiate and experimentally prove the possibility of a biosystem’s thermodynamic characteristics being inherited during the long stages of biological evolution when the environment remains practically unchangeable.  All types of tropisms in the universe are governed by hierarchy thermodynamics of complex systems. This takes place in animate and inanimate matter including cosmic objects in the universe.
The following are related quotes:
“The properties of living things are the outcome of their chemical and physical composition and configuration.”
— Thomas Morgan (1932) (Ѻ)
1. Gladyshev, G.P. (1988). Thermodynamics and Macrokinetics of Natural Hierarchical Processes. (287 pgs). Moscow: Nauka Publ., (in Russian).
2. Gladyshev, Georgi, P. (1997). Thermodynamic Theory of the Evolution of Living Beings,(appendix two).Commack, New York: Nova Science Publishers.
3. Gladyshev, Georgi, P. (1978). "On the Thermodynamics of Biological Evolution", Journal of Theoretical Biology, Vol. 75, Issue 4, Dec 21, pp. 425-441.
4. Schlesinger, William H. (1991). Biogeochemistry – an Analysis of Global Change. New York: Academic Press.
5. Gladyshev. (2007). Hierarchical thermodynamics - general theory of existence and living world development
6. (a) Thims, Libb. (2007). Human Chemistry (Volume One), (preview). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview). Morrisville, NC: LuLu.
(c) Press release: World’s first-ever textbook on the Chemistry of Love - September 27, 2007, 3:00 EST (PR.com).