  We introduce a pathwise approach to analyze the relative performance of an
equity portfolio with respect to a benchmark market portfolio. In this
energy-entropy framework, the relative performance is decomposed into three
components: a volatility term, a relative entropy term measuring the distance
between the portfolio weights and the market capital distribution, and another
entropy term that can be controlled by the investor by adopting a suitable
rebalancing strategy. This framework leads to a class of portfolio strategies
that allows one to outperform, in the long run, a market that is diverse and
sufficiently volatile in the sense of stochastic portfolio theory. The
framework is illustrated with several empirical examples.
