We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema...

I defend the idea that the fact that no system is entirely isolated (“Interventionism”) can be used to explain the successful use of the microcanonical distribution in statistical mechanics. The argument turns on claims about what is needed for an adequate explanation of this fact: I argue in particular that various competing explanations do not meet reasonable conditions of adequacy, and that ...

3 Thermodynamic State Variables and State Equations 8 3.1 State Variables and Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 Exhaustive set of state variables? . . . . . . . . . . . . . . . . . . . . 8 3.1.2 Are state variables de ned only in equilibrium? . . . . . . . . . . . . 11 3.1.3 Concept of local equilibrium . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.4 C...

For the description in terms of a flowing ground state plus excitations see Lecture 15 and problem 3 of Homework 7 for Ph127a. This approach has some disadvantages. Conceptually, it has the problem that we calculate superflow in terms of what it isn’t, i.e. the excitations which reduce the mass flow! The superflow is slipped in by Galilean boost arguments. Practically, the approach is limited t...

The satissability of random CNF formulae with precisely k variables per clause (\k-SAT") is a popular testbed for the performance of search algorithms. Formulae have M clauses from N variables, randomly negated, keeping the ratio = M=N xed. For k = 2, this model has been proven to have a sharp threshold at = 1 between formulae which are almost aways satissable and formulae which are almost neve...

Statistical mechanics provides the link between microscopic properties of many-particle systems and macroscopic properties such as pressure and temperature. Observations of similar "microscopic" quantities exist for the motion of zooplankton, as well as many species of other social animals. Herein, we propose to take average squared velocities as the definition of the "ecological temperature" o...

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generaliz...

A manifest covariant equilibrium statistical mechanics is constructed starting with a 8N dimensional extended phase space which is reduced to the 6N physical degrees of freedom using the Poincaré-invariant constrained Hamiltonian dynamics describing the micro-dynamics of the system. The reduction of the extended phase space is initiated forcing the particles on energy shell and fixing their ind...

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generaliz...

Recent reports using single-cell profiling have indicated a remarkably dynamic view of pluripotent stem cell identity. Here, we argue that the pluripotent state is not well defined at the single-cell level but rather is a statistical property of stem cell populations, amenable to analysis using the tools of statistical mechanics and information theory.