Economics is an extremely broad field, encompassing things that are closely related to psychology (e.g. behavioral economics), and things that are related to physics and natural science (e.g ecological economics), as well as pure mathematics (e.g. game theory) so trying to say it has more in common with one than the other is kind of a vacuous statement or category error.
To those who are angry at normative claims and policy prescriptions from the economic orthodoxy/zeitgeist, I understand your frustration. I would say what you’re angry at is not economics itself (which is simply the study of scarcity and related human behavior) but economics done badly. Such as the Chicago school.
Setting aside the emotional baggage related to these issues, there are some really beautiful and fascinating topics in economics that borrow very directly from statistical physics in the analysis of financial time series data (and also apply to a wide variety of fields like network traffic, the distribution of metals in ore, turbulent flows in fluid dynamics, and the distribution of galaxies in space), originally identified by Benoit Mandelbrot.