History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
Philosophy of thermal and statistical physics Philosophy of thermal and statistical physics The philosophy of thermal and statistical physics is that part of the philosophy of physics whose subject matter is classical thermodynamics, statistical mechanics, and related theories. Its central questions include: What is entropy, and what does the second law of thermodynamics say about it? Does either thermodynamics or statistical mechanics contain an element of time-irreversibility? If so, what does statistical mechanics tell us about the arrow of time? Thermodynamics is the study of the macroscopic behaviour of physical systems under the influence of exchange of work and heat with other systems or their environment.