Albert Einstein

Albert Einstein's research into statistical physics has had a very great influence on science. His theory of Brownian motion, though not perfect, influenced Smoluchowski to formulate his equation, which these days would be called diffusion with drift. Einstein omitted to write the drift term in the heat equation, and expressed equilibrium as the balance between the diffusion current and the drift. This leads to his famous relation between the diffusion constant, the external field and the drift velocity.

Einstein saw immediately that the paper of Bose was essentially advocating a new counting method for particles, and he wrote his paper on condensation within a few months of that of Bose. He predicted that superfluidity would occur (at low enough temperatures).

Einstein's celebrated work of the dynamics of the absorption and emission of photons gives relations that are confirmed by quantum electrodynamics. His theory is not formulated as a Markov chain, however, since the transition probability is deemed to be proportional to the mean energy of the ambient electromagnetic field. Thus, in Einstein's model the dynamical law depends on the statistical state (and so on the temperature). For a Markov chain the transition probability depends on the microscopic state occupied by the system, not on the statistical state at the previous time. In this sense, Einstein's model is a non-linear Markov chain.

Einstein remarked in his (under-rated, if you read his biographers) Ph. D. work that heat is essentially the thermalised energy of oscillators, a view that I share, and use in my concept of "heat-particle". See my book called Statistical Dynamics.