Cosmology Group Podcasts

David Albert begins with a brief discussion of an issue raised in the last lecture- whether you can define an entropy for a non-equilibrium system. He and Tim Maudlin agree that while the steps along the reversible route must involve equilbrium states, partitioning can still be used to define the entroy of a non-equilibrium system.

Tim returns to the discussion of statistical mechanics began in the last lecture, addressing how we can calculate and explain the velocity distribution of gas particles at equilibrium. Following work by Boltzman and Maxwell, we can model the gas as a system of particles that colide, and calculate the 'critical areas' which particles of a given velocity must be in if they are to colide with other gas particles in a given time. We then have a dynamics for how a velocity distribution will evolve. By assuming the 'Stosszahlansatz'', that the number of particles in the critical areas is proportional to the number of particles in the system, we can show the system will evolve towards a particular distribution.

In this lecture, David Albert continues his introduction to thermodynamics, explaining how the entropy of a system is defined and determined in thermodynamic terms. This requires distinguishing between reversible and irreversible paths between two states of a system, and envisaging how pistons and heat baths can be used to mimic the irreversible transfer of heat between a warm body and a cool one. Tim Maudlin and David disagree on whether the entropy of a non-equilibrium system can be defined.

Tim begins his discussion of statistical mechanics by considering equilibrium states- where the macroscopic description of the state no longer changes over time. (He also introduces the problem of the adiabatic piston--for some systems, it is controversial to define the equilibrium state.) We then consider how the macroscopic thermodynamic properties of the gas can be understood using a statistical mechanical model, which treat the gas as a system of monotonic moving particles. At equilibrium, such a system will tend towards the Maxwell-Boltzmann state, where the velocities of gas particles are randomly distributed. He argues that in order to explain this, we need to appeal to the dynamics of the system, and how the particles are interacting. Appeal to statistics, without dynamics, are not enough.

This is the second lecture in the joint NYU/Columbia graduate course on philosophy of statistical explanation and cosmology. It's David Albert's first lecture, and in it he introduces the main ideas he'll discuss in the class, with some contrast between his approach and that of our other lecturer, Tim Maudlin (NYU).