At first, it seems obvious to assume that exothermic reactions are precisely those reactions that take place voluntarily, and that the more heat is released, the more violent they become. In many cases, chemical reactions do indeed behave in this way. This experience led to the formulation of the principle of Thomsen and Berthelot in the early years of thermochemistry. This empirical - but not strictly valid - rule states that if reactants are brought together under isobaric and isothermal conditions so that a chemical reaction can proceed, then the resulting new equilibrium state is characterized by the fact that the process leading to it releases more heat than any other possible process. In other words, of all possible processes, the most exothermic is realized. The principle is also equivalent to saying that the realized process should make the enthalpy difference 
as large as possible and thus the resulting enthalpy 
small as possible.
The existence of voluntarily occurring endothermic reactions (for example, an evaporating liquid) shows, of course, that this principle cannot claim general validity. The actual criterion is: Those reactions take place voluntarily which lead to an increase in the total entropy of the system and its environment. Under isobaric and isothermal conditions, this criterion of total entropy maximization is equivalent to minimizing the Gibbs energy of the system. A reaction that reduces the Gibbs energy of the system is called an exergonic reaction. The distinction between voluntary and involuntary reactions is equivalent to the distinction between exergonic and endergonic reactions.
An example of a chemical reaction that is endothermic but nevertheless voluntary is the decomposition of dinitrogen trioxide into nitrogen monoxide and nitrogen dioxide:
The enthalpy of reaction Δ 
of this decay is positive, so the reaction is endothermic. The Gibbs reaction energy Δ 
, however, is negative, so the reaction is exergonic.
The change in Gibbs energy 
is under isothermal conditions
.
At small temperatures, Δ 
and minimizing the Gibbs energy 
is approximately equivalent to minimizing the enthalpy 
of the system. In this case, the exergonic reactions are usually also exothermic reactions, and the principle of Thomsen and Berthelot predicts the equilibrium states approximately correctly by considering the enthalpy change. Even at higher temperatures (such as room temperature), the principle remains approximately correct, since the temperature dependences of Δ 
and Δ 
are similar at temperatures that are not too high (as can be shown by considering the Third Law), and the similarity of Δ and Δ therefore preserved with temperature increase over a larger temperature range.
However, if a reaction is accompanied by a sufficiently large entropy increase Δ 
(as in the aforementioned cases of evaporating liquid or the decay of dinitrogen trioxide), then the term may 
predominate and the reaction may proceed voluntarily (exergonic, Δ 
), although its enthalpy increases in the process (endothermic, Δ 
), i.e. the reaction "runs uphill" in terms of enthalpy.
